{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-06T14:01:22.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-04-06T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":50489,"title":"Find the area between curves (P1)","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none 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width=\"62.5\" height=\"18\" style=\"width: 62.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e)          \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = AreaCurves(a, b)\r\n  \r\nend","test_suite":"%%\r\nfiletext = fileread('AreaCurves.m');\r\nfor ii = [3.5773, 6.1773, 5.5773, 11.2970]\r\n    assert(isempty(strfind(filetext, num2str(ii))), ... \r\n    'Do NOT use provided answers in your solution')\r\nend\r\n%%\r\na = 1; \r\nb = 1;\r\n\r\ny_correct = 3.5773;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 3; \r\nb = 0.3; \r\n\r\ny_correct = 6.1773;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = -1;\r\nb = 4;\r\n\r\ny_correct = 5.5773;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = pi;\r\nb = exp(1);\r\n\r\ny_correct = 11.2970;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":487522,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":25,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-19T12:36:27.000Z","updated_at":"2026-01-23T10:01:56.000Z","published_at":"2021-02-19T12:40:47.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eArea between curves - Problem 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the area between the curves \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x) = x^2\\\\, \\\\mathrm{e}^{- x^2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e  and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg(x) = a\\\\, x + b\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e over the interval [0 2] for different \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e  and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e coefficients:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                                                                                                                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"420\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"560\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e     \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                        plot of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea=b=1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e)          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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1261,"title":"Find 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When you solve this type of problem you must use both quad and the trapz functions (easy), returning the absolute value of their difference which should be zero.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":56255,"title":"Area under the curve","description":"Compute area under the curve specified by points stored in y, where y is in range (0,inf) and x time step is 1. \r\nnote: please round the result to 4 decimals.\r\nexample: y=[1 2 3 5 8 9 10]\r\n                area=32.5000","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 111px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 55.5px; transform-origin: 407px 55.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCompute area under the curve specified by points stored in \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ey, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ey\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is in range (0,inf) and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e time step is 1. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003enote: please round the result to 4 decimals.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eexample: y=[1 2 3 5 8 9 10]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                area=32.5000\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function area = your_fcn_name(y)\r\n  area= 'Your solution'\r\nend","test_suite":"%%\r\nx = [1 2 3 5 8 9 10];\r\ny_correct = 32.5000;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\n\r\nx = [43    10    27    16    29    45    53    46    88    52    95    64    96    25    68    29    68];\r\ny_correct = 798.5000;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\n\r\nx=[70     7    26    23    67    85    35    79    68     1];\r\ny_correct = 425.5000;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\n\r\nx=[0.993183755212665   0.480756369506705   0.827750131864470   0.603238265822881   0.817841681068066   0.955547170535556   0.650378193390669 0.627647346270777   0.646563331304310   0.062133128691720];\r\ny_correct = 6.1374;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":1739584,"edited_by":1739584,"edited_at":"2022-10-10T12:14:42.000Z","deleted_by":null,"deleted_at":null,"solvers_count":26,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-10-10T12:13:31.000Z","updated_at":"2026-03-05T14:10:14.000Z","published_at":"2022-10-10T12:14:42.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCompute area under the curve specified by points stored in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e is in range (0,inf) and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e time step is 1. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enote: please round the result to 4 decimals.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eexample: y=[1 2 3 5 8 9 10]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e                area=32.5000\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":50504,"title":"Find the area between curves (P3)","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 541px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 270.5px; transform-origin: 407px 270.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20px; border-block-end-color: rgb(60, 60, 60); border-block-start-color: rgb(60, 60, 60); border-bottom-color: rgb(60, 60, 60); border-inline-end-color: rgb(60, 60, 60); border-inline-start-color: rgb(60, 60, 60); border-left-color: rgb(60, 60, 60); border-right-color: rgb(60, 60, 60); border-top-color: rgb(60, 60, 60); caret-color: rgb(60, 60, 60); color: rgb(60, 60, 60); column-rule-color: rgb(60, 60, 60); font-family: Helvetica, Arial, sans-serif; font-size: 20px; font-weight: 700; line-height: 20px; margin-block-end: 5px; margin-block-start: 3px; margin-bottom: 5px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 3px; outline-color: rgb(60, 60, 60); perspective-origin: 384px 10px; text-align: left; text-decoration: none; text-decoration-color: rgb(60, 60, 60); transform-origin: 384px 10px; white-space: pre-wrap; margin-left: 4px; margin-top: 3px; margin-bottom: 5px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eArea between curves - Problem 3\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFind the area enclosed by the curves \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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src=\"data:image/png;base64,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\" width=\"62.5\" height=\"19\" style=\"width: 62.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e for different \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; 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width=\"87.5\" height=\"18\" style=\"width: 87.5px; height: 18px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = AreaCurves(a, b)\r\n  \r\nend","test_suite":"%%\r\nfiletext = fileread('AreaCurves.m');\r\nfor ii = [0.4208, 0.5101, 0.2569, 0.1252, 1.1838]\r\n    assert(isempty(strfind(filetext, num2str(ii))),'Do NOT use provided answers in your solution')\r\nend\r\nassert(isempty(strfind(filetext, 'if')),'if: Forbidden')\r\nassert(isempty(strfind(filetext, 'switch')),'switch: Forbidden')\r\n%%\r\na = 1; \r\nb = 0.5;\r\n\r\ny_correct = 0.4208;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 2; \r\nb = 0.5; \r\n\r\ny_correct = 0.5101;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = exp(1); \r\nb = 1; \r\n\r\ny_correct = 0.2569;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 0.5;\r\nb = 0.4;\r\n\r\ny_correct = 0.1252;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = sqrt(2);\r\nb = 0.1;\r\n\r\ny_correct = 1.1838;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":0,"created_by":487522,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-19T18:50:42.000Z","updated_at":"2026-02-05T14:11:12.000Z","published_at":"2021-02-19T18:51:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eArea between curves - Problem 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the area enclosed by the curves \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x) = sin(ax)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg(x) = bx\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for different \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e  and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e coefficients\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":50499,"title":"Find the area between curves (P2)","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 612.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 306.25px; transform-origin: 407px 306.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20px; border-block-end-color: rgb(60, 60, 60); border-block-start-color: rgb(60, 60, 60); border-bottom-color: rgb(60, 60, 60); border-inline-end-color: rgb(60, 60, 60); border-inline-start-color: rgb(60, 60, 60); border-left-color: rgb(60, 60, 60); border-right-color: rgb(60, 60, 60); border-top-color: rgb(60, 60, 60); caret-color: rgb(60, 60, 60); color: rgb(60, 60, 60); column-rule-color: rgb(60, 60, 60); font-family: Helvetica, Arial, sans-serif; font-size: 20px; font-weight: 700; line-height: 20px; margin-block-end: 5px; margin-block-start: 3px; margin-bottom: 5px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 3px; outline-color: rgb(60, 60, 60); perspective-origin: 384px 10px; text-align: left; text-decoration: none; text-decoration-color: rgb(60, 60, 60); transform-origin: 384px 10px; white-space: pre-wrap; margin-left: 4px; margin-top: 3px; margin-bottom: 5px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e Area between curves - Problem 2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 32.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 16.25px; text-align: left; transform-origin: 384px 16.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e Find the area enclosed by the curves \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAH8AAAAoCAYAAADXNiVcAAAG+0lEQVR4Xu2aBYilVRiGn7XFLmxFVOxO7E5UFLu7u8Uu7MIWxU4UO1CxsAsTE+zC7g6e5Ttyd/afmXPuf2dn9t57YNlh5vwnvvfL9zvD6I6OlcCwjr159+J0we9gJeiC3wW/gyXQwVfvWn4X/A6WQAdffbAt3/2XAD4BPmoBDjMC0wPPAP+2YL22XmIwwR8L2AX4BrihRWCNAWwOjA1cDfzV1ujVvFwrwHeNWYHlgSmB14BHgJ/7OJvA7wN82kLg03aeZ1NgvK4C9K0ddcEfHzgAWBrYD5gFuAc4Azgc+L2X7QVnGeCQfpSkWd32XCcCdwEPNbtIu39XB/wxgf0DdMF8LH4+E7gZ2BH4vkKAswNnAQcBbwyggOcATgH2Bd4fwH2GytILAKsAi8Nw8m5vYF7gKGAeYFvgzsbD1gF/0QD5YWDPsODJgXWBp4C3KqSiwhwN/AqcCvw9gJLzbnqjSYFjB3ivAbxG0dLLAY+G1zWBHgf4GLgPOL6nHJoFP4F4JLAlcG3mEdXAS4DdgFcyv6kzbX7gQmBn4PU6C40m324BnAZcB7wDXAasBdwObADc2grLN7ZfD2jpGxYAqSUuBOwB/DgKBDoRcD7wUoSadi7/tPKTw9tdEbnYt+EFxGiTnt64WctXi24Jd7IV8FUGkJMAlwIvAidlzG/VlMOAhfvIQVq1z2CvM1144KmBHSL0Jpn/AuwF/FDX8hs17ILQsN8ybq4LNhE8ELgjY36rppiDnABsDLzZqkWH4DpWXPcCFwNHRKU1J3BTuP/zeuY9uZZv6WSGLinT2+hPEVYFrgTWAV7IEN4EwGLA+sDqwFQ9MlZduhWDIeSB0OwvK9ZdJLLcbWJextZDYspkwFLARsAKgAZmTE+ymwY4LjgNY/tnAbou/v64gR5a0K3GfgI+AL5Ot8sFv1EaS8biCn+1AoFuHaXhSLGnF1HPEL//M5IYw4usnWD/E6FDpZQeliV0/Q8r1rLkuxGwBL2qEFaFfU3hN1XT5TSeKFzHkvg7QNdtkrxi3NkkWzJNLsWqSaN6LnKo2UIOlrbJQ1uVnQ3MFF7Bb4aPZsBXyFqwGqhGvZt5KQ+9UmivzF7J0ONcFHuqBHoPSxiTzv6SOAUifWzGa7lTMgYT/HROKyvPbe5yN7B7cBfex7LOMXNk+CqBxJnkWuJhlLteW+UfgXcpBb/xIH0ROVUC9hDGJQX6v+vJRCK57mlDe00wj8nk7qeIREjLKwU/83gDPs28RbBfBV4OQs3kuT/F7/NgpeCn7NG4InHiv9wD1AE/ZbLGPkklrd9OYM5oB/BTsmwoMHSNlLnnCKLnnFLwkwvVEnX5xtLcUcft26QxxunydGGHAn9kbpxivmcdlSVm5vGyppn8me+sHXmTMqg9SsFP9KHsUQm540FLE77Gy3lOM3u5eqnKXG7BNRL4Ml+5TGRtwbZ4gXGB04NGt5STLPs/cWt2r1LwU+L1YPTNq0qr3s5SWuo1rpP6CCY2pYpnnvF4tJxtPpWMoZDwed71wvKtsGyXe67SpHmke5eA3yy5kzZNFmiXqYTkkbE6J0rK7aP2LeknWFrqNUoqk3TmoQD+XBGu5OUNWxMCazZROtYCvzHu7BpZd4kVJZ797ei15ySKPvo4OFqyZrvGfb2PQjCHsN5fNjjrLyoOk6oTq4TUeSw582DPleiSr7eysjFl3F8DSPJXPtb/PlsbgbrNOXiJ5SeqcL4mXajnkXM2afF/mw49h+eZOGhIXwJtBkgqWbsa41LYSXHfLqFEk0xX1cMRyRAFpvBkwYb68BmaFZVsnuSWD2VUcGt0R6r3jfv+zXBgNSOLl2NMI9y/BHxjtrThkxHvpQpLh93Ay8Oan634eEHgtugW6iFk7Gz/Jqv2oYJ/15L1BFKWCqHK6l1+5fAQPmQYHR50aBgSVwL/Xli0ni89iUsNNTuiGsDnQf709WSuV4xKwDfDVAPrZJvphYmvbKueeRnfde2SGrJy5gdeMA3pXB+DWDl4eX/u7dWvGbIPRnxTWJsQKdXyJuebF9mCtu3t/1Yoja1v+xv+Tm+nESkrqe2mRi74jY2dkmSr6lApgbN0eb6pU+d9ZFkqLyAhUlKV5K3eBrNywU8Mm0pgHNYl1RmWXzZofME7EMCMKgWrI4NB/zYX/NQrtjvUivdw7mvWOnckK7298m1GQCqojzbNgKWCixOhZjYdHb+pAl8ixWdAPq7cLvrEAm7yJLMmydKK4d726eWtz20FYwUIvG7eZNKOVxf4PpCqAj910My0dfH2gSVZdNGphdgK8NMaPkqwjKt65l26j6WdiV5u06d0/baaXwW+xIF1+E7A04BEg+D7CLI72kgCuTG/ja7cvUqSQBf8DtaFLvhd8DtYAh189f8AQYWAOJHhcZoAAAAASUVORK5CYII=\" width=\"63.5\" height=\"20\" style=\"width: 63.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"68\" height=\"32\" style=\"width: 68px; height: 32px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; 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src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEEAAAAmCAYAAACbBvanAAAE3UlEQVRoQ+2ZB4hkRRCGvzOLmBWzIp4oimJWzCgGEAVFzDnnHBGzYk6YD8WEGFAwoaJiwoyKiGIEc8KEqJjTt1bLeNdvXve8gTuOaVh22Omurvqruuqv2nGMFuNGGDACwSAYRcIIhH+TweSOBO9fHfgE+GgI+WkRYCHgeeCvUnmTE4TpgH2Bb4Bba5TuY9w0wA7A9MBNwO8lQAwDBGUsAawHzAO8BjwO/NhHAQE4FPh0iACk69RnO2CmUiC6gjAzcCSwFnA4sDhwP3ABcALwSwMQKrk2cGwLWCWOzO1RrzOB+4BH24R0AWFa4IgwXqOejM8XAncAewHfZRRYErgIOBp4o03BDt8vBZwDHAa8309OFxBWCWMfAw4Kj84FbAE8C7yVuVjgTgZ+As4F/uhgZNtRbTM65wBO7XfXoCAkY04EdgJubtMovl8WmADsD7xaeKbLtuWBK4F9gNebBA0Kgm//FkDPb11hkJ5ZETgQ+L6LdYVnZwUuB16JJ5gtm4OCsBVwJ/AgsDPwVYFSswPXAC8DZxXsH9aW44GV+uSogcjSDMDZ8d6uiOrwc4HGhqYJ8yjgnoL9w9pijjoD2AZ4Mye0NBIsOWZ0yU3TagNkI+AGYHPgpQILZwFWBbYENgHmBXYD7o2zhroVxqf1MHAw8GVG7spxZtfYN8mWUhB6D64BPASoxMZNgjPK7BIldduGyjHxkYXjD78B58WzkwVq9J/xpHSOtFvWqfwPM/daKm8DLN03domE3rNepkf1pvzg3QKvusVKsgGwYzDFwmNj24zAq+JOc5DR9HEk57YeYXyw0ruB04cBgqVRQSabfoQod5cgyCwF4esaBIAU0gsAV0ciPqWwN5g7SvjTwwIhZXjLogTEnzZPJHu7gLBgGLI+IDkzGuw8S9bQQUihpWd8Cr610tXlOdgM2Y8cEAn6OODXwotTTlDXbGmuTYzrAk8A71SSJPWtTYy9NqqnlcBeoIabKCOBYHLNMttaEFKCeiT69lxJanJQbYnslZP6lMUGcIB56Klo9W3yJlk1IAxKktKlySMnVZKl+YBLohTvAaxZ2a9Yko2ixkpWA8KcMaTYDNgvsnThsxzblnj829HrlyRUhy/HRCtsiTMvGI2+bXOMfGGd4B1fZJRJ1cyqkjrdTpGwNHA7sFy/0GpBZU9AEP39bUNkzhZtr5Op7QHJmcMX2+/0HFNesCuVsJ3WMMBx0iXBspxf26RbTST4pmWKz0Q++KAmDGKv3ed14d0XMudXAO6K7tSIkQHadicvrxbf61kj44foXXJRoPgNI2Kk242DlRoQbIOlnpIVP+uZ2uV9hwBOhXPjN9+/IW/T4/DV/PF5zyXSZIcyVhqjwc9NU+oZY3DjzNPutfH5lYLQ20DVDFFyIKVEdz7wYi2KFfst5/KKpsbqP1GlICTGJhi+0/cqlMlttWzZCDlxrimzpddWAV0Kgko/AFzcNq8r1NJ7NwWWAS7rM5UuFPe/bTrK4ar/gJFit1ahHAgSkusjQ+8OfBaGm2Tk7LLFYSzvdk7gsOXSAXPMxHoIgOFv0pXZtgKggBwIqWMzMxv6iwZZMXQVPOw1fwCQG8/X3mVJNCGWNldj8nMgSFCs43sDzwFOeGRsDiunylWaE6ZK45NRIxCmgH/NTxERNoqEf9zwNyXzCTaE4DDAAAAAAElFTkSuQmCC\" 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src=\"data:image/png;base64,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\" width=\"29.5\" height=\"19\" style=\"width: 29.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"76.5\" height=\"18\" style=\"width: 76.5px; height: 18px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = AreaCurves(a, n)\r\n  \r\nend","test_suite":"%%\r\nfiletext = fileread('AreaCurves.m');\r\nfor ii = [0.5, 0.6667, 1.3606, 2.7754, 22.3242]\r\n    assert(isempty(strfind(filetext, num2str(ii))),'Do NOT use provided answers in your solution')\r\nend\r\n\r\n%%\r\na = 1; \r\nn = 3;\r\n\r\ny_correct = 0.5;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 1; \r\nn = 5; \r\n\r\ny_correct = 0.6667;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 2; \r\nn = 2.5; \r\n\r\ny_correct = 1.3606;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = pi;\r\nn = 3.1;\r\n\r\ny_correct = 2.7754;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = exp(3);\r\nn = 12;\r\n\r\ny_correct = 22.3242;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":1,"created_by":487522,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-19T15:56:21.000Z","updated_at":"2025-08-25T11:22:08.000Z","published_at":"2021-02-19T15:59:16.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e Area between curves - Problem 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e Find the area enclosed by the curves \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x) = x^{n}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg(x) = ax^{\\\\frac{1}{n}}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e for different \\\"n\\\"  and \\\"a\\\" coefficients\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"420\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"560\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                       Plot of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and  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the area between curves (P4)","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 601px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 300.5px; transform-origin: 407px 300.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20px; border-block-end-color: rgb(60, 60, 60); border-block-start-color: rgb(60, 60, 60); border-bottom-color: rgb(60, 60, 60); border-inline-end-color: rgb(60, 60, 60); border-inline-start-color: rgb(60, 60, 60); border-left-color: rgb(60, 60, 60); border-right-color: rgb(60, 60, 60); border-top-color: rgb(60, 60, 60); caret-color: rgb(60, 60, 60); color: rgb(60, 60, 60); column-rule-color: rgb(60, 60, 60); font-family: Helvetica, Arial, sans-serif; font-size: 20px; font-weight: 700; line-height: 20px; margin-block-end: 5px; margin-block-start: 3px; margin-bottom: 5px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 3px; outline-color: rgb(60, 60, 60); perspective-origin: 384px 10px; text-align: left; text-decoration: none; text-decoration-color: rgb(60, 60, 60); transform-origin: 384px 10px; white-space: pre-wrap; margin-left: 4px; margin-top: 3px; margin-bottom: 5px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eArea between curves - Problem 4\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFind the area enclosed by the curves \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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\" 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style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"126\" height=\"18\" style=\"width: 126px; height: 18px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = AreaCurves(a, b, c)\r\n  \r\nend","test_suite":"%%\r\nfiletext = fileread('AreaCurves.m');\r\nfor ii = [6.5065, 6.3475, 0.1134, 9.4710, 4.0104]\r\n    assert(isempty(strfind(filetext, num2str(ii))),'Do NOT use provided answers in your solution')\r\nend\r\nassert(isempty(strfind(filetext, 'if')),'if: Forbidden')\r\nassert(isempty(strfind(filetext, 'switch')),'switch: Forbidden')\r\n%%\r\na = 1;\r\nb = 1;\r\nc = -2;\r\n\r\ny_correct = 6.5065;\r\nassert(abs(AreaCurves(a,b,c)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 1;\r\nb = 2.5;\r\nc = -5; \r\n\r\ny_correct = 6.3475;\r\nassert(abs(AreaCurves(a,b,c)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 0;\r\nb = 4.8;\r\nc = -0.5; \r\n\r\ny_correct = 0.1134;\r\nassert(abs(AreaCurves(a,b,c)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = pi;\r\nb = pi;\r\nc = -pi;\r\n\r\ny_correct = 9.4710;\r\nassert(abs(AreaCurves(a,b,c)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 2;\r\nb = 70;\r\nc = -6;\r\n\r\ny_correct = 4.0104;\r\nassert(abs(AreaCurves(a,b,c)-y_correct)\u003c1e-4)\r\n\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":487522,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-20T22:13:12.000Z","updated_at":"2026-01-18T15:37:37.000Z","published_at":"2021-02-20T22:13:59.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eArea between curves - Problem 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the area enclosed by the curves \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = y^4 - a\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = bx + c\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for different \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e coefficients\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc 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vertically even-degree polynomial's graph by its mean over an interval","description":"Let p be an even-degree polynomial with positive leading coefficient. Consider its vertical translation by shifting its graph by its average value over a specified interval [a, b], with a\u003cb.\r\nThe interval [a, b] is defined such that the endpoints a and b stand for the least and the greatest x-values of the equation p(x) = y_peak, the lowest and the largest real solutions, respectively. Here, y_peak stands for the highest local maximum of the polynomial p (see non-scale figures below). \r\nGiven p, return \r\nthe endpoints a and b if they exist. Otherwise, return a = '' and b = '' (see Hint 1);\r\nthe shifting constant, k, which stands for the above vertical translation (see Hint 2). Return k = '' if the interval is empty.\r\nHint 1. An n-degree polynomial has exactly n roots (counting multiplicity) in the complex number system. An odd-degree polynomial always has at least one real root. Therefore, a real polynomial of even degree always has at least one vertex, but might not have local maxima.\r\nHint 2. To calculate the mean of a continuous function, use the integral definition.\r\ninput: p\r\noutput: [a, b, k]\r\n ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 662.112px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 331.05px; transform-origin: 408px 331.056px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLet \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e be an even-degree polynomial with positive leading coefficient. Consider its vertical translation by shifting its graph by its average value over a specified interval \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[a, b], \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewith \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea\u0026lt;b\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe interval \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[a, b] \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eis defined such that the endpoints \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eb\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stand for the least and the greatest \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-values of the equation \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep(x) = y_peak\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the lowest and the largest real solutions, respectively. Here, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ey_peak\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the highest local maximum of the polynomial \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(see non-scale figures below). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, return \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 61.3125px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 30.65px; transform-origin: 391px 30.6562px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethe endpoints \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eb\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if they exist. Otherwise, return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea = ''\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eb = '' \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(see Hint 1);\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethe shifting constant, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ek\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which stands for the above vertical translation (see Hint 2). Return k = '' if the interval is empty.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint 1. An \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-degree polynomial has exactly \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e roots (counting multiplicity) in the complex number system. An odd-degree polynomial always has at least one real root. Therefore, a real polynomial of even degree always has at least one vertex, but might not have local maxima.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint 2. To calculate the mean of a continuous function, use the integral definition.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[a, b, k]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 264.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 132.4px; text-align: left; transform-origin: 384px 132.4px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"370\" height=\"259\" style=\"vertical-align: baseline;width: 370px;height: 259px\" 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [a, b, k] = Vshift(p)\r\n  a = x;\r\n  b = x;\r\n  k = x;\r\nend","test_suite":"%%\r\np = [0.25 -1 -2 0 0];\r\na_correct = 2*(1-sqrt(3));\r\nb_correct = 2*(1+sqrt(3));\r\nk_correct = 64/5;\r\n[a, b, k] = Vshift(p);\r\ntolerance = 1e-13;\r\nassert(abs(a - a_correct) \u003c tolerance)\r\nassert(abs(b - b_correct) \u003c tolerance)\r\nassert(abs(k - k_correct) \u003c tolerance)\r\n\r\n%%\r\np = [0.25 -2 1.5 10 0];\r\na_correct = 2-3*sqrt(2);\r\nb_correct = 2+3*sqrt(2);\r\nk_correct = -3.2;\r\n[a, b, k] = Vshift(p);\r\ntolerance = 1e-13;\r\nassert(abs(a - a_correct) \u003c tolerance)\r\nassert(abs(b - b_correct) \u003c tolerance)\r\nassert(abs(k - k_correct) \u003c tolerance)\r\n\r\n%%\r\nfiletext = fileread('Vshift.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\np = [1 0 0 0 -1];\r\noutput_correct = ['', '', ''];\r\nassert(isequal(Vshift(p), output_correct))\r\n\r\n%%\r\np = [0.5 3 7.5 11 11 8 4];\r\noutput_correct = ['', '', ''];\r\nassert(isequal(Vshift(p), output_correct))\r\n\r\n%%\r\np = [1 -8.5 14 34 -72 0 -17.5];\r\na_correct = -2.094230059318471;\r\nb_correct = 4.727773843365965;\r\nk_correct = 29.244170120692807;\r\n[a, b, k] = Vshift(p);\r\ntolerance = 1e-13;\r\nassert(abs(a - a_correct) \u003c tolerance)\r\nassert(abs(b - b_correct) \u003c tolerance)\r\nassert(abs(k - k_correct) \u003c tolerance)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2026-01-09T14:11:42.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-01-03T12:06:01.000Z","updated_at":"2026-03-25T12:52:10.000Z","published_at":"2026-01-09T14:11:42.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e be an even-degree polynomial with positive leading coefficient. Consider its vertical translation by shifting its graph by its average value over a specified interval \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[a, b], \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ewith \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u0026lt;b\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe interval \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[a, b] \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eis defined such that the endpoints \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stand for the least and the greatest \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-values of the equation \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep(x) = y_peak\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, the lowest and the largest real solutions, respectively. Here, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey_peak\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the highest local maximum of the polynomial \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(see non-scale figures below). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, return \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethe endpoints \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if they exist. Otherwise, return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea = ''\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb = '' \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(see Hint 1);\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethe shifting constant, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, which stands for the above vertical translation (see Hint 2). Return k = '' if the interval is empty.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint 1. An \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-degree polynomial has exactly \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e roots (counting multiplicity) in the complex number system. An odd-degree polynomial always has at least one real root. Therefore, a real polynomial of even degree always has at least one vertex, but might not have local maxima.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint 2. To calculate the mean of a continuous function, use the integral definition.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[a, b, k]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"259\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"370\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"Vertical shift\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"259\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" 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\",\"relationship\":null},{\"partUri\":\"/media/image2.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58259,"title":"Easy Sequences 115: Integral involving square root, floor, and round functions","description":"Given a postive real number , we are asked to evaluate the following integral:\r\n                            \r\n                            where:     the symbol \"\" is the floor function,\r\n                                            and \"\" is the round (to the nearest integer) function.\r\nWe may rewrite the above function in Matlab as:\r\n\u003e\u003e  S = @(n) round(integral(@(x) sqrt(floor(x))-floor(sqrt(x)),0,n));\r\nTherefore, for , we have:\r\n\u003e\u003e  s = S(10*pi)\r\ns =\r\n        12\r\nBe careful though, in using the Matlab integral function, as it is only an approximation. For example if :\r\n\u003e\u003e  s = S(100000)\r\n\r\nWarning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is\r\n8.0e+01. The integral may not exist, or it may be difficult to approximate numerically to the\r\nrequested accuracy. \r\n\u003e In integralCalc/iterateScalarValued (line 372)\r\nIn integralCalc/vadapt (line 132)\r\nIn integralCalc (line 75)\r\nIn integral (line 87)\r\nIn @(n)round(integral(@(x)sqrt(floor(x))-floor(sqrt(x)),0,n)) \r\n\r\ns =\r\n       49841\r\nThe correct answer is . The integral function is off by only 2 units here, but the discrepancy could be even greater for other values of . integral function can also be quite slow. The challenge is to find an efficient and more accurate algorithm to evaluate the integral.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 673px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 445.71875px 336.5px; transform-origin: 445.71875px 336.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven a postive real number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, we are asked to evaluate the following integral:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 48px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 24px; text-align: left; transform-origin: 384px 24px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-18px\"\u003e\u003cimg 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SltoamfiOwiOBW5yOgciPBK43G0XNaCj5In/XyEGcrTHPC5b93X5eyD8k4v7wTy3wVEiR0N0yFGyOjL8jv+b2PZPnuHejraM7iV1ibI8SkdnoN+cGOBqiwk7gmdto4Ehb9tcAPwcoIP+HsBBqAmX+r8G3Ac8Yok5htZhsspdgKdyqpsDlbCBTDXV52Vr0KZrkUD7+wFc3TkNmA+Y/ACRNqDeWyCNOjbWjqiw3ctYy4vXEyVfnHBxssXzsKzSAcM5UT4GeNvFEdQm12A3jhYJjpJsxIRoReFSxsIUkMThmTEcZFSaMXFJ29r0K9sxJOQ9B+qtHZLnJx3q9Kh7t5/h4hwAMe8DwGbVLis0+CFSqc9OuxppBN9x9pVt2XwuGkPeicfiGpZzHgeQvI5oFzuo1QCTixBh+hBLqCFkmZfWsN9A7PMuYJxdW2UZnCFNqnKfoqizk51dhzGnYF/jzZ9osK+h050M1CP1HpuJqJz2DarHiIh9R7iyWf7TETpMXgxQh1xXEvbjxifD9ko7pJjPuqzuPimVy4Fp77iygsvmPHGCF/HxSHvNFdIX4ZYuniRogxI7mnoRuXQQYsQmSCOZcYOMZ739nvfiwWiHS6jkvP2Z9YWBQsjxUJf2IEI68ErSzylY/ZX0Lb8RfFvdZQ950XHVxqRIzvs9GHWJM4yOnCs7lLWAo4E/A5OBPIXn2rUAB8o2g909TwNKXhf7WQ6aKDye1lGfgHhPoJ5Zd9GPzRy0z2QLRDa1jRrDUdiPM1W7RlhM2c9FcmTnB9vTRXiQfdkIG2MBLs2Zk3kTcc4cbanOH/UjOVb4YAZJrVdeqqIAOm92cHsBXEoMkw29RI7+o+QZZHwJ4InweJQS0s15v454cAme+9sy+D2ujMsRXgNMdtvBgEv5lBmdQeLfRvCd2LiCK24VsO/hwHajN38BA04EegLfATgz+j7AlZx6OnrsXpOcjr3YX2wL0OFsDXDwQ/B63RdYF7gMkHRl4C0ksR/g5GhV4EjgOoD95SNAsB9BUmIp+rF5AS15GVgP4CSL5/VRgC9c/l7WJcRN3jiAJY8TgPMADoRY5u7AlUAPgNfOqQB9WdPK19CyTwHeF/blbGwwneCJVmT5fxhHOzkj4AkQFHYu7wDUeQLgwY0SdkDU+2OUAtI3czrUC+uovuvl05GfA/wNWAUIk75I/ASYB9jJG6ZXhrRxMJK8TC2Bsd92ttJeYmABbea9MLPvJMR5HscNKpM2gSP84IpbcF8OeHk98Jo6APgI2A+gHASYXTzmvCYWAnsCcTINmZPiFAqc1wHbZtdp3/rYfwlA7uYA57m48YrNRJLFsZmImmnXoEQWVK/EAR/LN5zpFdEd8Yu9POqMBlYC2oCRwEYAz0X29xxoM50yA6D+fIBpPK95jtGhZyXtKNja0SerSiqVO94ZMQchnRxldYDOhsaFOSckF0o4+zUieSB3BngQ6aT3AbhMznyuLGwBxAlPoleAtwE7OYL6vnMeFczE9k8Bs+dBxFkWZylRcggyqH9+lEKJ0svkvHmR23FaUFCON4VdHNiZnQwPTsHWJM77ZVfvewhpA89rE3ZY7wO0h/mLgAlAJWl1501+bgD84zkd29U6miyOTdbOuyfaeWeg7a9i+w6A/mZhII8cPQQc6aW/izj7+/UBk3MRMT7Zd7McP9/00gwL4byvQovYWIJOhmR9CHCU/UugF1BkWQ3G8cD9BrgJ4MHlNh21PfzA7QcAdoRJ5CdQ4j5fjVC+2eWz01ohRGdfpFmHy9n0riE6ftK92GB9cQ7e1y9yvEzOm+c6eSf+UGBSb/XsnIl4tR19WNOSOO9ZXr3XIR5cFeLA3vjjtdcdqCTToDCpklJB8ztgV70zbzZte8B4Y8gZZrWSxbGZCCNoz6BqjalCf3nocpLCwZ7PwV+wvTnAPvsN4BLgywDP9UMA0+Uy+C6ALwOwYX09b01w+TxrKYTzHoZWrutaugHCkcAeAGffZRA676M8Qzm6GwGcBJwN0AFvA1TT4W0AfQ5kngfagFpkC+zEkyzMufvlDcYGT0wOCJpByuK8eT7YQI/8/7DA5PN6tM7r8JTsTOK82QfsB2wSUSc5pG3BzjRC/bNkOe9OdiYh4DF9FggOijo14n+zODZ5OG9r1YqI8LwZDqxpiQjpeLliGpSdkEDdXsEMt80yeK6uEZGfdnIhnHfajWqW8v4VDeHF5Q8MsmjbFBTKQcLKWRTegDLL4rx5z9AcIsPBDeCqmipvg/JdQJLZbZJykzjvJOVUqyPn3ckYndQCYJ9qCcxQP0/nnWEzcim6Ic671plkLowUqJLfwpafARcAjwO8L5W2nI4COaLksvo7aReu8mIZ2MrL/Qjxx7ztIkZHFdEo2VQzAw9iT3/GWXNB2rF1GKhliaZ12Fm6pSdjk077dsBuLSytUfvWGOx6FnACwNmIJF8GtvSqm4H4+962omJADIiBwjEg5538kHBGdhAwF6ADT2vJcjeUdTkwHrgYkOTPgO+8H86/etUoBsSAGKiOAS2bV8fXG1AfAuwP8N5oGsIy9wL4tLOkMQzIeXc+GNQ7QD/P8fcCabVscpIQ9nARHyiViAExUAMDct7Vk/Yhdrml+t0i93guMkcZeTCwHCrxn6BuxZn3P8DBWIcg53ww7ivBxCq22ce8AkQ9+dtRRVlSFQNiwDEg561TodUZ2AwE2N9R+JKIOS1IyHFo80Yh7U7j4T2WcSIwIKR8zuzvD0lXkhgQAxUYkPOuQJCym54B/u/fpBVn3Wz79UZARuHVGZWrYsVAyzLAe1ESMdDKDPjOm3/ZkYgBMSAGCs+AnHfhD5EMzJiBL3nlawnXI0NRMSAGisuAnHdxj40sy54BvtJzO1fNmwifyr5K1SAGxIAYqJ8B3fOun0OVUF4GBsL0VZz5UxB+EtIU/sXpQGA4wHfT3w1cBywGJGJADIiBhjAg590Q2lVpQRjYwbPjHi9uUf4P+VZgY+AwgNcLHTffdc8X9vBvgxIxIAbEQO4MyHnnTrkqLBADfI+8CWfUQeH77IcCdNR/dpn8WxXfdX8mcIpLU9CaDKyDZj8S0XS+3GaviLyiJI+HIVH/4eeAVSIGxECLMjAO7eZ/eacWtP18jzzt+2uIffxMIT8Qwy9u+YPcHthmx/w6wO8RS1qTgb+g2Xy5TRReKgEtE2Pst3bZMyElaE7DTGxHzexHiD4Ns0IVi4EUGSiy8+6Ldn4M8IKbENLm0S7vvpA8+/7y/iF5ShIDYqC1GGiI89bT5q11kqm1XzDAB9Ds/P/dF8mfx/gwG2VeZ7DUb4fbMp2lMrUhBsSAGMiaAeu8sq5H5YuBojGwrzOIjjjszWq8n0lZ1Bks9fu22+q/VKo2xIAYEAM5MSDnnRPRqqZQDPAvX+a8r0A87C9idj+b9/6CYk+Z8764RAyIATGQOwNy3rlTrgpzZIDL2tOBl4F9vHrHIL4qwAfPLvHS/egCt7Gyn+ji5rQXhuQpSQyIATGQOQNy3plTrAoayMABqJvvLl8X4F+8KN2B4z+Ldet2AcJXXTwYzHcJYU+PWprpBPfVthgQA2IgUwbkvDOlV4U3mAHfudqrT8+CTVsCTwDnxth3r8ujblAsbXIwQ9tiQAyIATEgBsrOwDg0gH/FmtqghiyHeh9wNlyK8HqA97efBNYGKslMKFB/DU9xTcTZpqe9NEXFgBhoXQb0V7HWPfZqeUYM8MGyocBYgKtMfOkK4zsArwCVhMvrHwFneIrjXdqJXpqiYkAMiAExIAaahoFGz7zTIPIIFDIbuM1hLsLDAYkYEANigAw0ZObdJu7FgBiIZeBa5BKbA/yE6CxAIgbEgBhoKANy3g2lX5WXiAG+y1oiBsSAGCgEA7wPKBEDYkAMiAExIAZKxICcd4kOlkwVA2JADIgBMUAG5Lx1HogBMSAGxIAYKBkDuuddsgNWUnNXgt27V7D9ReTzNaYSMSAGxIAYEANioIEM2F/F+FKTSjitgXaqajEgBsRArQy0Y0fr3+zVybWWlXg/zbwTUyXFGhhYjH2IJPJxEiXpiAExIAYKxgAdN/s59mFLCmabzBEDYkAMiAExIAbEgBgQA2JADIgBMSAGxIAYEANiQAyIATHQCgz8E4wZzfzxYlQVAAAAAElFTkSuQmCC\" width=\"247.5\" height=\"48\" style=\"width: 247.5px; height: 48px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                            where:     the symbol \"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAC8AAAAmCAYAAABUKMJkAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAL6ADAAQAAAABAAAAJgAAAADlRKSGAAAA/ElEQVRYCe2YPQrCQBSE4x9YaG8teAXxEp7AO0hu4xWsbTyDWHkPK8VO1Fmw2qx5m+dIECawxc6bN/vyJdUWhR4REIGYwBbCKhZ/uJ8i+4A1YZxxRciGEZSZsYTviTW3/F3LgHrnvTKsVMvQSssZ3spora7h20Iv8iLvIKDfxgGN0iLyFIyOEJF3QKO0iDwFoyNE5B3QKC0iT8HoCBF5BzRKi8hTMDpCRN4BjdLy1+T7mQgG8I0ib7iSu0Va0224FYtnGDcNqfOfUQyDpta+rtGolag/PuSGsxZGf+WtU/41xFmicId2TOi50g7G8DV7iYYLtFNClyQC3xJ4ASZiG5LKUdtBAAAAAElFTkSuQmCC\" width=\"23.5\" height=\"19\" style=\"width: 23.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\" is the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/help/matlab/ref/floor.html#\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003efloor\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e function,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                                            and \"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAC8AAAAmCAYAAABUKMJkAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAL6ADAAQAAAABAAAAJgAAAADlRKSGAAABA0lEQVRYCe2YPQrCQBCFg2hnL0hajyBY2VqIpVXuIHgbLyB4A09gZSNYCdZiEbDRTtC3aDWs2WR2xAhv4BF2fl6GL6k2SRgkQAKSwAqJTCYNzlN47KGDRzvkulBhNAurr+IYjwu0LNFbpeWM5iMkd+gg14dS6ARFxRXTiyiHasMTtD+gYWisEWqoc53L/+rrkDzJKwjwt1FAMxkheROMChOSV0AzGSF5E4wKE5JXQDMZIXkTjAoTkldAMxkheROMChOSV0AzGflr8vKq7RORFgptUXS3WjeRq90xx0ZuUZ/WX9h29H7XIORdhvwMJj2P0R25rScfm9rAYA65m2IGCVgTeAIWdR8c5SIdFQAAAABJRU5ErkJggg==\" width=\"23.5\" height=\"19\" style=\"width: 23.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\" is the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/help/matlab/ref/round.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eround \u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e(to the nearest integer) function.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWe may rewrite the above function in Matlab as:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u0026gt;\u0026gt;  S = @(n) round(integral(@(x) sqrt(floor(x))-floor(sqrt(x)),0,n));\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTherefore, for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"53\" height=\"18\" style=\"width: 53px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, we have:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 60px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 442.71875px 30px; transform-origin: 442.71875px 30px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u0026gt;\u0026gt;  s = S(10*pi)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003es =\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e        12\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eBe careful though, in using the Matlab \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/help/matlab/ref/integral.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eintegral \u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003efunction, as it is only an approximation. For example if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"74\" height=\"18\" style=\"width: 74px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 260px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 442.71875px 130px; transform-origin: 442.71875px 130px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u0026gt;\u0026gt;  s = S(100000)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eWarning: Reached the \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003elimit on the maximum number of intervals in use. Approximate bound on error is\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e8.0e+01. The integral \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003emay not exist\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e, or \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eit may be difficult to approximate numerically to the\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003erequested \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eaccuracy. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u0026gt; In integralCalc/iterateScalarValued (line 372)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eIn \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eintegralCalc/vadapt (line 132)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eIn \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eintegralCalc (line 75)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eIn \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eintegral (line 87)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eIn \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003e@(n)round(integral(@(x)sqrt(floor(x))-floor(sqrt(x)),0,n)) \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003es =\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e       49841\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe correct answer is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"65\" height=\"18\" style=\"width: 65px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. The \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eintegral\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e function is off by only 2 units here, but the discrepancy could be even greater for other values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eintegral\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e function can also be quite slow. The challenge is to find an efficient and more accurate algorithm to evaluate the integral.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = S(n)\r\n    % NOTE: the following expression is inaccurate for some values of n\r\n    s = round(integral(@(x) sqrt(floor(x))-floor(sqrt(x)),0,n)); \r\nend","test_suite":"%%\r\nn = 1:20;\r\ns_correct = [0 0 0 1 1 1 2 2 3 3 3 4 4 5 6 6 6 7 7 7];\r\nassert(isequal(arrayfun(@S,n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = (1:20).*pi;\r\ns_correct = [1 2 3 4 6 7 8 11 11 12 15 16 17 18 20 22 23 24 26 28];\r\nassert(isequal(arrayfun(@S,n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = 100*exp(1);\r\ns_correct = 126;\r\nassert(isequal(S(n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = 1234.5678;\r\ns_correct = 601;\r\nassert(isequal(S(n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = 12345.6789;\r\ns_correct = 6125;\r\nassert(isequal(S(n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = 100000;\r\ns_correct = 49839;\r\nassert(isequal(S(n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = 6e6;\r\ns_correct = 2998571;\r\nassert(isequal(S(n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = 4e8*pi;\r\ns_correct = 628304194;\r\nassert(isequal(S(n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = 10.^(1:10);\r\ns_correct = 5555500618;\r\nassert(isequal(sum(arrayfun(@S,n)),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = (1:1e5).*exp(2);\r\ns = arrayfun(@S,n);\r\nss = round([sum(s) nnz(s) mean(s) median(s) mode(s) std(s) sum(num2str(s))]);\r\nss_correct = [18444149135 100000 184441 184439 303161 106553 37072130];\r\nassert(isequal(ss,ss_correct))\r\nassert(isempty(lastwarn))","published":true,"deleted":false,"likes_count":0,"comments_count":8,"created_by":255988,"edited_by":255988,"edited_at":"2023-05-18T18:10:19.000Z","deleted_by":null,"deleted_at":null,"solvers_count":1,"test_suite_updated_at":"2023-05-18T18:10:19.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-05-04T18:21:04.000Z","updated_at":"2023-05-18T18:10:26.000Z","published_at":"2023-05-05T19:51:12.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven a postive real number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, we are asked to evaluate the following integral:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es=S(n)=\\\\Bigg\\\\lfloor\\\\ \\\\int_0^n\\\\sqrt{\\\\lfloor{x}\\\\rfloor} - \\\\Big\\\\lfloor{\\\\sqrt{x} \\\\Big\\\\rfloor\\\\ \\\\mathrm{d}x\\\\  \\\\Bigg\\\\rceil \\\\cdot\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                            where:     the symbol \\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\lfloor\\\\ \\\\rfloor\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e\\\" is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/matlab/ref/floor.html#\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efloor\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e function,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                            and \\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\lfloor\\\\ \\\\rceil\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e\\\" is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/matlab/ref/round.html\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eround \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e(to the nearest integer) function.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe may rewrite the above function in Matlab as:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[\u003e\u003e  S = @(n) round(integral(@(x) sqrt(floor(x))-floor(sqrt(x)),0,n));]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTherefore, for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=10\\\\pi\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, we have:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[\u003e\u003e  s = S(10*pi)\\ns =\\n        12]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBe careful though, in using the Matlab \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/matlab/ref/integral.html\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eintegral \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003efunction, as it is only an approximation. For example if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=100000\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[\u003e\u003e  s = S(100000)\\n\\nWarning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is\\n8.0e+01. The integral may not exist, or it may be difficult to approximate numerically to the\\nrequested accuracy. \\n\u003e In integralCalc/iterateScalarValued (line 372)\\nIn integralCalc/vadapt (line 132)\\nIn integralCalc (line 75)\\nIn integral (line 87)\\nIn @(n)round(integral(@(x)sqrt(floor(x))-floor(sqrt(x)),0,n)) \\n\\ns =\\n       49841]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe correct answer is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es=49839\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eintegral\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e function is off by only 2 units here, but the discrepancy could be even greater for other values of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eintegral\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e function can also be quite slow. The challenge is to find an efficient and more accurate algorithm to evaluate the integral.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":55335,"title":"Generate Bernoulli polynomials","description":"The Bernoulli polynomial  is a polynomial of order  with the properties that  and for  \r\n,\r\nwhere the prime denotes differentiation with respect to , and\r\n.\r\nTherefore, , , , etc. Notice that  is the th Bernoulli number.\r\nWrite a function to generate the Bernoulli polynomial of order . Use MATLAB's approach for specifying the coefficients. For example, the function should return [1 -1/2] for  and [1 -1 1/6] for .","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 201px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 100.5px; transform-origin: 407px 100.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 78.5917px 8px; transform-origin: 78.5917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Bernoulli polynomial \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEkAAAAoCAYAAACy29cjAAAE00lEQVRoQ+2Zu8tVRxTF/f6CGGMlBMRHJyiJj0Ybi2giWCka0lgEfIEgSMSopFADGkWw8IWFjZoQ0wQSooKNFgYTSCqbaGGtEZM/QNdPZsswzGOfc+6NQc6Bxf3uPTN79qzZs/ae+WZmjU+TgZlmi7HBrJEkRxCMJL0FJL2nORwRDgtPHfNpNflEDd4XLrQaxu//z5EEQVeE/cKfXSbVaPuF3s8Xdnlttkha7TD074QnwZAQ9IuwV7jr8KFrk7Pq8Ew46OnoIeljGfoyMfZbCH8ms1x4KFwUrguPPAM32nwbbLom0XO8v9Rvj/Bzq3+LJOvPqq4LX27oc31kmH3+U/gOeVsGErVV/VnpxWEhWnPo+55d8qNnHC9Jf8vYu8GbHfpMhY9J7Qzvv9bnkAhghYnKE31n36HffbUFVX3ykLRARthO9izTH6mQIobHo2ha0cHRuClRdE2YO+UosjFd43lIMkMYhqxFGQJikkptPLyxqqT6eDt7+vVtg6Y+EXK747VND0mIKDrDc07IhWa83VLN8k7AIpaU/19sNfOruTAekmI9+lSWIS1+mByCbZq1QX83M0aGOYvYNXrXNe3jwzzhQYjE2DwCXStTbIGLXLRIWqoB/ohGTLUCB04LlAE8ORK9kWRbNqd5ORv4tl34SFgYGsRJg/c/hHfURPiYK0+a47ZISgX5Kw20JDi0OQyMBn0j3Co44SXJyoyWT2aP6HkeIoeMCFH4skp4RyC6kQekYk5AzheIPi8UI7jlUFwfWQHJQIi3rR6OUBIMPTp0JSmecLyY+PWdcEpIpSFHErvhjlAU7xpJpvxmON0GcRFJOG8UumpJ7PQQkmyi2GMxbwreWs36FhNGjaSUBEI2fY7pBzuyWKj3Pa0PIQm/XgTnWLCcr7ko4rdBJMUEEL5kn/RJhb1vZsPuUJKsP5HUpZhtZtVaJJkYMoFasWUrSLshRxJblL7VttVzRFKXc5/pWWfh9hxFICWNpGrlWor38Hszy1T6W19r0iWibXE610meowgOxe347q1xcvM1wrsSbf2sBOga0WxTklRxi5bY8xxFcCbekrXjCOJomY9J8eRKBuyRmby3hkzuV8HuhXK6REV9UsgVkpbBqzJRIik+iuQM2N2zXY/kMhtRtk3gHgoCPxO4jl0pcITJaQChj81admJr8dwTLgnfC3bWS+ulfXpXu4G0DE4UFi8LcySl+5tsQaX9T3COm0omYmc1isnSRb05TQ3ygUC5sEngWqV0DoTw0vEmrodwJ826qUaWsnKYyqtic7ZQvXWISUKsYZ7P1nNbDR4LHEVqdZGFP5F0VGDL2VYu6RfR9GHBcYtgfMSH3G0BC7O28t7mZsmpqaOtY0mLrNr7uGKPtyxbGeTupbBnOnMoEDrEh1pfFvB3oVmZT5Mk2+9x3WLboXQvZZOyEzwn/En8YyElC0n5XHAVndMkyeqP+ExkeuepYyCZrIXg9z3q5CKJBUDw0SGX3WmSxI0fdzhx5jA9oqrmP7OtVM+EEPlJEYW9A8JuL0GwPC2STI/ScxRHGLIXtdBVwXNrgC3XijvEC7HuvH2nRRKpGuG9LMR3Opa5zuj3Ple8Dh4m32RaJE3e0zdocSTJQf5I0kiSgwFHkzGSRpIcDDiajJHkIOkl3/gcOG9yxJsAAAAASUVORK5CYII=\" alt=\"B_n(x)\" style=\"width: 36.5px; height: 20px;\" width=\"36.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 76.2417px 8px; transform-origin: 76.2417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a polynomial of order \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 74.675px 8px; transform-origin: 74.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with the properties that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"B_0(x) = 1\" style=\"width: 62.5px; height: 20px;\" width=\"62.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25.6667px 8px; transform-origin: 25.6667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEkAAAAkCAYAAADFGRdYAAADeklEQVRoQ+2YuYoVQRSGZx5AXCMxcgkGBA3USARNFH0AHUwExS0WdzAQdzTTcYKByVQ0VRRBA0MNZiIDl9DI5RH0/6XOcLruqbqna/reG9wqOPSd7tNV1V//Z+mZnKijL4HJvh7VYaJCcoigQqqQHAQcLlVJFVKSwFpcmQpXP+P4K8dq3JS0GzCuwgjpOWwl7AxsBjYH+27BGidIRwDgCewN7KhSzzb8XoD9ge2wQI0LJAFBoWyHLUaKOY+/78A+wXbGahoFpI0pWTtyaKnLa9y4PwUB57mnb2Hy0zjO6oVGAekvNnAzlwNKSSTu0yriulcSfl9xfpMFchSQfmMjq8NGhwHrBta6HNabxvFpAhLPHw7XCGspiXsgsRJsgOk4pjzXw34UhA7nOw67qGCxulDica7oQlQSapzLykeyhuQl/t2AaUE6CKetsH2wXeFBJE4J5xGM8c3BirC38OEsWKw8FwrnSwHVyvVCaoSlBUlUMo9VKTsOHlfA3sNuh3OsBhy5OE9tXJ8fNCzmQBleSM9wA1uG/yMXbh9xnX0D3+5ZGMujqIZN2YcwRy7OPZDEZ1CwBBJVvyazIf1MLkjc8M8wIUPtBOw+TJLeKfx+HK6vwzHb1rchBd+uYWlIWzJ7ZZp5GfbqgqRvoJKY6akmGcxLbOd57UBLCF53gXUSN0jYU83XYK+8k8BvYOEmELgXNlmbo01JMmSSvdtiw21dmR/PhRci9zIHPsgoIl6jpLo1GspUTpLGigseit5cvxa/LQjLP4bDfHIJ9hZmfoRmFtUv3Ju4G89sQdIQGrEZNiL5qF8iLIHFtTk/Q5lD4LxooZx4Xfmw5fmeTw7lLIrr+dC1IOmkHKuIc8pkbAB1niqBIvfIvzB0/0XlLAeOzM3c9gXGLj+3Z0khPcKwIGmiccnUVU9KPyveLVhJtxzDYf671xEc/dKkm6ZKrAqnC1VPSFqQpBpY1LV0Wfqvh5BIfTSm1BXDYdXSLcZyVJm6V/o+K+REGGYhiiFpolao6VDkg/HNL3WmzifT1WYYcHTYcW02yBIFjAy+aObA5JdDDIkPfCzMavU/nPQhbBVsHpb6os7xolKHCSfeC59xD4wVlOMdjP1eMl14/gvgFIjbjZssgeteoGvHUUDq+hkGPl+F5EBcIVVIDgIOl6qkCslBwOFSlVQhOQg4XP4Bu/bLJWBU5hIAAAAASUVORK5CYII=\" alt=\"n \u003e 0\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"B'_n(x) = n B_{n-1}(x)\" style=\"width: 113.5px; height: 20px;\" width=\"113.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 169.858px 8px; transform-origin: 169.858px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere the prime denotes differentiation with respect to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 27px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 13.5px; text-align: left; transform-origin: 384px 13.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-8px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Integral[B_n(x),{x,0,1}] = 0\" style=\"width: 80px; height: 27px;\" width=\"80\" height=\"27\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 34.225px 8px; transform-origin: 34.225px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTherefore, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"B_1(x) = x-1/2\" style=\"width: 81px; height: 20px;\" width=\"81\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPMAAAAqCAYAAABmx23YAAAKP0lEQVR4Xu2d6+tvwxfHv+cPkOtTOrk8UIrcEw8ol5AUQqRT5J6S23F7ILcolMIh6iRCkRJyKR6Q3CMenHLphDxy/QtYr2OvWt/5zMyePTN725/Pd3atnN937z2zZs16r9us/fltWmtXk0CTwEpIYNNKrKItokmgSWCtgbkpQZPAikiggXlFNrIto0mggXnj6cD+suSjhfYT+lvoZaHfN54YVm/FDcyrt6exFV0gN18QersD9J7y3z+FLhZ6c2OJ4n9f7RXCwc815T53MO8ti71b6M5K3uN0GWdfoSf/962cnoHjZcrtQscYWT4u/76qA/RBlWQ8/cqWc8Y/hO2rhV6sxf6cwQyQnxe6RejrWguWcW4W2twJsuKwsx8K4L7u8QQoFR76DM+92S9qSRnEqTwntFcB/6RLP9r3+8CM4vdd5F3vugP3vdRzHyC/JXS90IeFY/leR7EJL28fYey5DokC+UJp5HxqA3PSthHdcJXqJPrHhWdOucDDyUJnC+0h9JfQs+5+9oGZidSKYL25AMETQoB4dyHCNO6Rh91TYaHMQejxg9CYYPtexr/OFUiKZFfsGQXzPrKuVgjzby4gvkMIo3elUEmaBjB/E0qJhDTN1FQI8OM4vfuUAmaWpxvOv18SopCiF+7+8w7QAP1EoZKwmLGxXGPncGzQaxPMM3fs/+PZ07nzPBV/6Da6CIj1KgUz+o3TO7BnEaqf6igvCoFYx0kFMxuu14XyDzdpv1f+dlv3gAv2oYLHYz4l9ODQFzOe/0zegVLDnYwpZv2KGs4jhct1+desuV5k7lD5025Cv1ZcB0AmtMUT8t9t3bSlYE6JOvXUgSmJgpP0MwXMCOorI78DPAIjt36gewYvfVSmMugipgr5pp4vUyyjvEYI94kQ4WO1iuoonPYPqpFjKdBCM+ElP6gAZgwE6eNhQqHo1eKN1LXXIyvTKWDmPEytUgioFsww2xdChISGlyQfOK1//6o8ofnLWEpQhcmRBiF8RKFK8r+RWBs87LKAGSxdFnF2amBxmFwx0C8IKQXMNl++T0bwFaWw7Od3o+eG2Wq1OIqaIsRWYUxtQAZr6ggvoFTUNmztY4RpJhtyWcCMrj0dMaDWKQ7GUQqYbb58gjDiluVtCFJSANOQ1zdHTCtseyKtiTb34965Qj8JhUJJbZxIkcVk2jlgIsKyY4U4WXCNIHtznNBHZt+QM0ccLpAZh6ukeOljW3nw7QE80Fbq7tuA5e96dBnArOGzL03V9VIvUq9MtXuHkG29/Ti2P30KzLHUG91MANVWmAkJLhXaKkTFjfD6nAJlUKuUGlrA2yVCnLtptdFaM1tEYAkhIQ6d1yqaKuNQ5XOfz4lE4Pvwbl0UsLhsuqBGir+THpG6UMihkmq7wLivVdvk/CxhwczPuKRcbtiofQTKd3KRJzDvMoCZIjFyCEVD1imyTGTCkZR7sZeE6gtGtw/MtkoNWAHLEd3oCiAmJe8qtei6IX08+fZT31WDc7A8tF2Ic+Qzhei0CQlRawJDIwL4sClIgn57H4Hnkk4ggPGdkB5hAFqAfpLQo0IYvC+FKKbYQqbLTCmgQuu3SqopFHL7QugboS0dnyW94csAZrxurNhoQ2xkiaw0YlHHqUVmr+PsAw4xvrWeO7sd29yBQz1yjYpoCZhtkQ5Qbu+UJKVTR5UtpwhWwzPTfFNahNKaBZuMAQPErvdFRoTioas01I0MvaYtozgDDAsRRc18fe5g1sarWO+EjaRCtSmr5ws5dQzMWpDSTXLDVNsswjM5YLAKUAJmW87H0w1pYFcwT114iyn/0Ht2k0vTnaFzpzyvxoa9AdhDTzs07w7NdbncQD/VWNQ2WKVHUyntmzbKi0WJahiR5br+gBiYbc4ZOm6ySrQweCdRW6CJFaJKwMxUusihR2OrAGZrzMYKl1NAG3rG6omv6ahvbDcE7Xs+dD+1HuO+XwJmTYP6PjO1YI7xaU+O1rWExsBs3X5IQVzv7W4UY2AUPhXSHDuUwJeCWRc5tGklt4qeq1BjvafGLBSipcxbApqYEbXGJqUn2QcmqvJ9npm6wHuR556Rezn95yVgRr9S2jct3mJgtnu0LhqOgVmVA9nErKk9urKKpNVWzY1sBROhu40hWmzL6f5yq6Ox8r+71yqcnAJYjZwZfnKq2XYdgOV9Ia1hDA1jdSxyu0NSUO95JhZ12ShvjMhhzjlzSvsm4rQgjRm8wWBOaeGEAbecbkFP8YxGEnvua8d1QVtSVcaq0UKqxbohoZwakb5ioE/H51LNhg8uXf8QY5aJ3eTX2PNXuqfha2galDLRXMGc0r6p67PYiNWfLJjXefCQAqe0cLrWhP9tlSj0/ax6chfMupihhTQNY6je6hHNEOuPIuDZc/rJa3jm0mo2hoyjrfuF9OhpiDFLAUvuMxox0fXEtc2AuuaHHXMFMzi6SSg1UtKmEV/kqntgTy7WnViEwGw9TigHs+ebTJSaqwHmUF7LYt4RSvpKRJ5Tq6/NKnahCFCVyY0QVDDam53Ke65Sj/Wem49paqTGDPkApBxDVYNnW8W1nkeNDcpOB1jpd+tzBXNf+6YrY+tEQ3mzAn7h9MUHZlVwncin6ITXjwhpWJfaR9p3pkvIS9dLqIkC3h7rGCNHxBvZKqFbNb1B7j8kFGrl1A63OYWlMRABCBoH8Go7hbZ2e6Bezhozzv4pvJR05Q0FNMZlixANIeTvGBFrSNTY4HleFRritWK8jA1m2wmZGjlqiD1Ut7S3w/fFlOq392sqF8wwcGMHKBUeR076yyL87bxOgfg3HjYGFncDNLcNeQoVQChMdHN0V7Budb1P8Cg/7aBTfaU1FBzu8zZfYl/OErKNMbbQ5LtfOn/f+zaiIzd2G1dsxdZ3v2/80P0xwQyQ73J0PuXnrHBMdEsO1S376yKAdrvQL0JU8zHkONeHhRaq8hbM+lFCikBp3B/6IbhWXPt+iaRPCJqn2o8HLM++jwt8axpSnEiRyRTPsNF8OEInV6hjS+UzZkdXaK2qQ6Hf41b+eb/m73WPBWaMZ+yKHXX1tW/26Yv9gIhnvxXaIRSsNeRUcPuY8N3XX9pM+Y2wqT6aRwEIB0vztRx5tHfqSgBHUfuXRko41Agy55g1e96pwEw4S46b2oOsha1TYpYoe9Vra30fiRcM3V5tEtj1u2FcqYXcKiKbAswszPeLFuQi/GxNqCOH+3w0UPOzPISmFV5ymZxuoCqCb4OstAQo9PW1b1YXwNhg1jNQ7QLTBRCGXCvk/t1doFZvawGa8W4VuqYBuboutQH/kwA6rXo/qUzGBLM9JvItKrWxgRy6lgdd+H8BmFTabbKNIIHU9s3qshgLzPoxdYzh0n7k6sJoAzYJVJAATVG5X2cVTT8WmIuYai83CSyxBEjlSn91J2v5DcxZYmsvNQnMTwINzPPbk8ZRk0CWBBqYs8TWXmoSmJ8EGpjntyeNoyaBLAk0MGeJrb3UJDA/CTQwz29PGkdNAlkS+BfgFIpJHsB+bgAAAABJRU5ErkJggg==\" alt=\"B_2(x) = x^2 – x + 1/6\" style=\"width: 121.5px; height: 21px;\" width=\"121.5\" height=\"21\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"B_3(x) = x^3 – 3 x^2/2 + x/2\" style=\"width: 149px; height: 21px;\" width=\"149\" height=\"21\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 52.4917px 8px; transform-origin: 52.4917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, etc. Notice that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"B_n(0)\" style=\"width: 36.5px; height: 20px;\" width=\"36.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 20.6083px 8px; transform-origin: 20.6083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.775px 8px; transform-origin: 7.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45831\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eBernoulli number\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 190.092px 8px; transform-origin: 190.092px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to generate the Bernoulli polynomial of order \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 188.658px 8px; transform-origin: 188.658px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Use MATLAB's approach for specifying the coefficients. For example, the function should return [1 -1/2] for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"n = 1\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 55.2167px 8px; transform-origin: 55.2167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and [1 -1 1/6] for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"n = 2\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = BernoulliPolynomial(n)\r\n  y = sum(nchoosek(n,k).*x.^(0:n));\r\nend","test_suite":"%%\r\nn = 0;\r\ny = BernoulliPolynomial(n);\r\ny_correct = 1;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 1;\r\ny = BernoulliPolynomial(n);\r\ny_correct = [1 -1/2];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 2;\r\ny = BernoulliPolynomial(n);\r\ny_correct = [1 -1 1/6];\r\nassert(all(abs(y-y_correct)\u003c1e-11))\r\n\r\n%%\r\nn = 3;\r\ny = BernoulliPolynomial(n);\r\ny_correct = [1 -3/2 1/2 0];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = 4;\r\ny = BernoulliPolynomial(n);\r\ny_correct = [1 -2 1 0 -1/30];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = 5;\r\ny = BernoulliPolynomial(n);\r\ny_correct = [1 -5/2 5/3 0 -1/6 0];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = 8;\r\ny = BernoulliPolynomial(n);\r\ny_correct = [1 -4 14/3 0 -7/3 0 2/3 0 -1/30];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = 11;\r\ny = BernoulliPolynomial(n);\r\ny_correct = [1 -11/2 55/6 0 -11 0 11 0 -11/2 0 5/6 0];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = 14;\r\ny = BernoulliPolynomial(n);\r\ny_correct = [1 -7 91/6 0 -1001/30 0 143/2 0 -1001/10 0 455/6 0 -691/30 0 7/6];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = 21;\r\ny = BernoulliPolynomial(n);\r\ny_correct = [1 -21/2 35 0 -399/2 0 1292 0 -6783 0 293930/11 0 -223193/3 0 135660 0 -1443183/10 0 219335/3 0 -1222277/110 0];\r\nassert(all(abs(y-y_correct)\u003c2e-9))\r\n\r\n%%\r\nn = 30;\r\ny = BernoulliPolynomial(n);\r\ny_correct = [1 -15 145/2 0 -1827/2 0 28275/2 0 -390195/2 0 4552275/2 0 -43785215/2 0 339319575/2 0 -2062720845/2 0 9509268925/2 0 -31795091601/2 0 72484065225/2 0 -102818379585/2 0 78132595905/2 0 -23749461029/2 0 8615841276005/14322];\r\nassert(all(abs(y-y_correct)\u003c1e-3))\r\n\r\n%%\r\nn = 12;\r\ny = BernoulliPolynomial(n);\r\nn2 = round(y(7));\r\ny2 = BernoulliPolynomial(n2);\r\ny2_15_correct = 373065;\r\nassert(isequal(round(y2(15)),y2_15_correct))\r\n\r\n%%\r\nfiletext = fileread('BernoulliPolynomial.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'switch') || contains(filetext,'regexp'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-09-17T15:39:23.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":"2022-09-17T15:39:23.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-08-20T20:19:44.000Z","updated_at":"2026-01-26T13:39:36.000Z","published_at":"2022-08-20T20:21:33.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Bernoulli polynomial \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B_n(x)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB_n(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a polynomial of order \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e with the properties that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B_0(x) = 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB_0(x) = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n \u0026gt; 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en \u0026gt; 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B'_n(x) = n B_{n-1}(x)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB\\\\prime_n(x) = nB_{n-1}(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere the prime denotes differentiation with respect to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Integral[B_n(x),{x,0,1}] = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\int_0^1 B_n(x) = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTherefore, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B_1(x) = x-1/2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB_1(x) = x – ½\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B_2(x) = x^2 – x + 1/6\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB_2(x) = x^2 – x + 1/6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B_3(x) = x^3 – 3 x^2/2 + x/2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB_3(x) = x^3 – 3 x^2/2 + x/2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, etc. Notice that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B_n(0)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB_n(0)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45831\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBernoulli number\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to generate the Bernoulli polynomial of order \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Use MATLAB's approach for specifying the coefficients. For example, the function should return [1 -1/2] for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n = 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and [1 -1 1/6] for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n = 2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59521,"title":"Integrate a power tower","description":"Write a function to compute this integral\r\n\r\nwhere . That is, the integrand is (x to the x) to the (x to the x) to the (x to the x)...","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 104px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 52px; transform-origin: 407px 52px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 122.783px 8px; transform-origin: 122.783px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute this integral\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"135\" height=\"44\" alt=\"I = integral((x^x)^(x^x)^(x^x)...,{x,a,0})\" style=\"width: 135px; height: 44px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"63\" height=\"18\" style=\"width: 63px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 226.3px 8px; transform-origin: 226.3px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. That is, the integrand is (x to the x) to the (x to the x) to the (x to the x)...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function I = intPowerTower(a)\r\n  I = integral(x^x^x^x^x^x^x^x,0,a);\r\nend","test_suite":"%%\r\na = 0;\r\nI = intPowerTower(a);\r\nassert(abs(I)\u003c1e-6)\r\n\r\n%%\r\na = 1/100;\r\nI = intPowerTower(a);\r\nI_correct = 0.00975627404012066;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 1/20;\r\nI = intPowerTower(a);\r\nI_correct = 0.04621245261821598;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 1/10;\r\nI = intPowerTower(a);\r\nI_correct = 0.0886781687569094;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 1/5;\r\nI = intPowerTower(a);\r\nI_correct = 0.1685639964895788;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 1/4;\r\nI = intPowerTower(a);\r\nI_correct = 0.2071658901263798;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 3/8;\r\nI = intPowerTower(a);\r\nI_correct = 0.30215124860335973;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 1/2;\r\nI = intPowerTower(a);\r\nI_correct = 0.3972053202401857;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 2/3;\r\nI = intPowerTower(a);\r\nI_correct = 0.5277402852630483;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 3/4;\r\nI = intPowerTower(a);\r\nI_correct = 0.5959989560650945;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 5/6;\r\nI = intPowerTower(a);\r\nI_correct = 0.6671963910854818;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 1;\r\nI = intPowerTower(a);\r\nI_correct = 0.822467033424113;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = (rand+3)/4;\r\nI = intPowerTower(a);\r\nI_correct = polyval([0.3875275 -0.9886411 1.132527 0.1505356 0.1405179],a);\r\nassert(abs(I-I_correct)\u003c5e-6)\r\n\r\n%%\r\nfiletext = fileread('intPowerTower.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp') || contains(filetext,'find') || contains(filetext,'switch'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":46909,"edited_by":46909,"edited_at":"2024-01-03T15:06:22.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-12-31T18:50:11.000Z","updated_at":"2026-01-28T06:58:04.000Z","published_at":"2023-12-31T18:50:21.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute this integral\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"I = integral((x^x)^(x^x)^(x^x)...,{x,a,0})\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eI = \\\\int_0^a {(x^x)^{(x^x)^{(x^x)\\\\ldots}} dx\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e0 \\\\le a \\\\le 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. That is, the integrand is (x to the x) to the (x to the x) to the (x to the x)...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59541,"title":"Compute the polylogarithm for real arguments","description":"The polylogarithm  appears in quantum statistics and quantum electrodynamics, and for special cases of  and , it connects to the logarithm, ratios of polynomials, the zeta function, the Dirichlet eta function, and other functions. \r\nWrite a function to compute the polylogarithm  for real arguments. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 74px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 37px; transform-origin: 407px 37px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 57.575px 8px; transform-origin: 57.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe polylogarithm \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"39\" height=\"20\" alt=\"Li_n(z)\" style=\"width: 39px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 267.225px 8px; transform-origin: 267.225px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e appears in quantum statistics and quantum electrodynamics, and for special cases of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ez\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.325px 8px; transform-origin: 9.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, it connects to the logarithm, ratios of polynomials, the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45988\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003ezeta\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45997\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003efunction\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 146.242px 8px; transform-origin: 146.242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the Dirichlet eta function, and other functions. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 142.233px 8px; transform-origin: 142.233px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the polylogarithm \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"39\" height=\"20\" alt=\"Li_n(z)\" style=\"width: 39px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 62.6167px 8px; transform-origin: 62.6167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for real arguments. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = polylogarithm(n,z)\r\n  y = sum(z^k/k^n);\r\nend","test_suite":"%%\r\nn = 2:2:16;\r\nz = 1;\r\ny = arrayfun(@(m) polylogarithm(m,z),n);\r\ny_correct = pi.^n.*[1/6 1/90 1/945 1/9450 1/93555 691/638512875 2/18243225 3617/325641566250];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = 3;\r\nz = 1;\r\ny = polylogarithm(n,z);\r\ny_correct = 1.202056903159594;\r\nassert(abs(y-y_correct)\u003c1e-12)\r\n\r\n%%\r\nn = 0;\r\nz = 1./(10:-1:2);\r\ny = arrayfun(@(s) polylogarithm(n,s),z);\r\ny_correct = 1./(9:-1:1);\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = 1;\r\nz = [-2 -3/2 -1 -1/2 0 1/10 1/7 1/5 1/3 1/2];\r\ny = arrayfun(@(s) polylogarithm(n,s),z);\r\ny_correct = [-1.098612288668110 -0.916290731874155 -0.693147180559945 -0.405465108108164 0 0.105360515657826 0.154150679827258 0.223143551314210 0.405465108108164 0.693147180559945];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = -1;\r\nz = [-2 -3/2 -1 -1/2 1/7 1/5 1/2];\r\ny = arrayfun(@(s) polylogarithm(n,s),z);\r\ny_correct = [-2/9 -6/25 -1/4 -2/9 7/36 5/16 2];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = -2;\r\nz = [-2 -3/2 -1 -1/2 0 1/17 1/13 1/11 1/5];\r\ny = arrayfun(@(s) polylogarithm(n,s),z);\r\ny_correct = [2/27 6/125 0 -2/27 0 153/2048 91/864 33/250 15/32];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = 1:3;\r\nz = 1/2;\r\ny = arrayfun(@(m) polylogarithm(m,z),n);\r\nzeta3 = 1.202056903159594;\r\ny_correct = [log(2) (pi^2-6*log(2)^2)/12 (4*log(2)^3-2*pi^2*log(2)+21*zeta3)/24];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = 2;\r\nz = -1;\r\ny = polylogarithm(n,z);\r\ny_correct = -pi^2/12;\r\nassert(abs(y-y_correct)\u003c1e-12)\r\n\r\n%%\r\nn = -1/pi;\r\nz = exp(-1);\r\ny = polylogarithm(n,z);\r\ny_correct = 0.6541056465726233;\r\nassert(abs(y-y_correct)\u003c1e-12)\r\n\r\n%%\r\nn = 4;\r\nz = 1/2;\r\ny = polylogarithm(n,z);\r\ny_correct = 0.5174790616738994;\r\nassert(abs(y-y_correct)\u003c1e-12)\r\n\r\n%%\r\nn = 1/2;\r\nz = 1/2;\r\ny = polylogarithm(n,z);\r\ny_correct = 0.8061267230428522;\r\nassert(abs(y-y_correct)\u003c1e-12)\r\n\r\n%%\r\nn = -3/2;\r\nz = -1./2.^(1:4);\r\ny = arrayfun(@(s) polylogarithm(n,s),z);\r\ny_correct = [-0.1516441361365191 -0.1313580923579523 -0.0892942267818043 -0.05260782861980105];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = 5*randn(1,randi(10));\r\nz = 0;\r\ny = arrayfun(@(m) polylogarithm(m,z),n);\r\ny_correct = zeros(size(n));\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nfiletext = fileread('polylogarithm.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2024-01-07T03:51:00.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-01-06T17:30:34.000Z","updated_at":"2025-02-27T16:14:20.000Z","published_at":"2024-01-06T17:31:22.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe polylogarithm \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Li_n(z)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e{\\\\rm Li}_n(z)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e appears in quantum statistics and quantum electrodynamics, and for special cases of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, it connects to the logarithm, ratios of polynomials, the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45988\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ezeta\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45997\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efunction\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, the Dirichlet eta function, and other functions. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the polylogarithm \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Li_n(z)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e{\\\\rm Li}_n(z)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for real arguments. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":50489,"title":"Find the area between curves (P1)","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 715.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 357.75px; transform-origin: 407px 357.75px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20px; border-block-end-color: rgb(60, 60, 60); border-block-start-color: rgb(60, 60, 60); border-bottom-color: rgb(60, 60, 60); border-inline-end-color: rgb(60, 60, 60); border-inline-start-color: rgb(60, 60, 60); border-left-color: rgb(60, 60, 60); border-right-color: rgb(60, 60, 60); border-top-color: rgb(60, 60, 60); caret-color: rgb(60, 60, 60); color: rgb(60, 60, 60); column-rule-color: rgb(60, 60, 60); font-family: Helvetica, Arial, sans-serif; font-size: 20px; font-weight: 700; line-height: 20px; margin-block-end: 5px; margin-block-start: 3px; margin-bottom: 5px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 3px; outline-color: rgb(60, 60, 60); perspective-origin: 384px 10px; text-align: left; text-decoration: none; text-decoration-color: rgb(60, 60, 60); transform-origin: 384px 10px; white-space: pre-wrap; margin-left: 4px; margin-top: 3px; margin-bottom: 5px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eArea between curves - Problem 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 24.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 12.25px; text-align: left; transform-origin: 384px 12.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFind the area between the curves \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"89\" height=\"24\" style=\"width: 89px; height: 24px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e  and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"89.5\" height=\"19\" style=\"width: 89.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e over the interval [0 2] for different \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e  and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eb\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e coefficients:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 447px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 223.5px; text-align: left; transform-origin: 384px 223.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                                                                                                                                \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"560\" height=\"420\" style=\"vertical-align: baseline;width: 560px;height: 420px\" 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width=\"62.5\" height=\"18\" style=\"width: 62.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e)          \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = AreaCurves(a, b)\r\n  \r\nend","test_suite":"%%\r\nfiletext = fileread('AreaCurves.m');\r\nfor ii = [3.5773, 6.1773, 5.5773, 11.2970]\r\n    assert(isempty(strfind(filetext, num2str(ii))), ... \r\n    'Do NOT use provided answers in your solution')\r\nend\r\n%%\r\na = 1; \r\nb = 1;\r\n\r\ny_correct = 3.5773;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 3; \r\nb = 0.3; \r\n\r\ny_correct = 6.1773;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = -1;\r\nb = 4;\r\n\r\ny_correct = 5.5773;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = pi;\r\nb = exp(1);\r\n\r\ny_correct = 11.2970;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":487522,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":25,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-19T12:36:27.000Z","updated_at":"2026-01-23T10:01:56.000Z","published_at":"2021-02-19T12:40:47.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eArea between curves - Problem 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the area between the curves \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x) = x^2\\\\, \\\\mathrm{e}^{- x^2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e  and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg(x) = a\\\\, x + b\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e over the interval [0 2] for different \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e  and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e coefficients:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                                                                                                                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"420\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"560\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e     \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                        plot of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea=b=1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e)          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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1261,"title":"Find 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When you solve this type of problem you must use both quad and the trapz functions (easy), returning the absolute value of their difference which should be zero.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":56255,"title":"Area under the curve","description":"Compute area under the curve specified by points stored in y, where y is in range (0,inf) and x time step is 1. \r\nnote: please round the result to 4 decimals.\r\nexample: y=[1 2 3 5 8 9 10]\r\n                area=32.5000","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 111px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 55.5px; transform-origin: 407px 55.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCompute area under the curve specified by points stored in \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ey, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ey\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is in range (0,inf) and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e time step is 1. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003enote: please round the result to 4 decimals.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eexample: y=[1 2 3 5 8 9 10]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                area=32.5000\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function area = your_fcn_name(y)\r\n  area= 'Your solution'\r\nend","test_suite":"%%\r\nx = [1 2 3 5 8 9 10];\r\ny_correct = 32.5000;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\n\r\nx = [43    10    27    16    29    45    53    46    88    52    95    64    96    25    68    29    68];\r\ny_correct = 798.5000;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\n\r\nx=[70     7    26    23    67    85    35    79    68     1];\r\ny_correct = 425.5000;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\n\r\nx=[0.993183755212665   0.480756369506705   0.827750131864470   0.603238265822881   0.817841681068066   0.955547170535556   0.650378193390669 0.627647346270777   0.646563331304310   0.062133128691720];\r\ny_correct = 6.1374;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":1739584,"edited_by":1739584,"edited_at":"2022-10-10T12:14:42.000Z","deleted_by":null,"deleted_at":null,"solvers_count":26,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-10-10T12:13:31.000Z","updated_at":"2026-03-05T14:10:14.000Z","published_at":"2022-10-10T12:14:42.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCompute area under the curve specified by points stored in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e is in range (0,inf) and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e time step is 1. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enote: please round the result to 4 decimals.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eexample: y=[1 2 3 5 8 9 10]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e                area=32.5000\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":50504,"title":"Find the area between curves (P3)","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 541px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 270.5px; transform-origin: 407px 270.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20px; border-block-end-color: rgb(60, 60, 60); border-block-start-color: rgb(60, 60, 60); border-bottom-color: rgb(60, 60, 60); border-inline-end-color: rgb(60, 60, 60); border-inline-start-color: rgb(60, 60, 60); border-left-color: rgb(60, 60, 60); border-right-color: rgb(60, 60, 60); border-top-color: rgb(60, 60, 60); caret-color: rgb(60, 60, 60); color: rgb(60, 60, 60); column-rule-color: rgb(60, 60, 60); font-family: Helvetica, Arial, sans-serif; font-size: 20px; font-weight: 700; line-height: 20px; margin-block-end: 5px; margin-block-start: 3px; margin-bottom: 5px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 3px; outline-color: rgb(60, 60, 60); perspective-origin: 384px 10px; text-align: left; text-decoration: none; text-decoration-color: rgb(60, 60, 60); transform-origin: 384px 10px; white-space: pre-wrap; margin-left: 4px; margin-top: 3px; margin-bottom: 5px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eArea between curves - Problem 3\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFind the area enclosed by the curves \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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src=\"data:image/png;base64,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\" width=\"62.5\" height=\"19\" style=\"width: 62.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e for different \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; 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width=\"87.5\" height=\"18\" style=\"width: 87.5px; height: 18px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = AreaCurves(a, b)\r\n  \r\nend","test_suite":"%%\r\nfiletext = fileread('AreaCurves.m');\r\nfor ii = [0.4208, 0.5101, 0.2569, 0.1252, 1.1838]\r\n    assert(isempty(strfind(filetext, num2str(ii))),'Do NOT use provided answers in your solution')\r\nend\r\nassert(isempty(strfind(filetext, 'if')),'if: Forbidden')\r\nassert(isempty(strfind(filetext, 'switch')),'switch: Forbidden')\r\n%%\r\na = 1; \r\nb = 0.5;\r\n\r\ny_correct = 0.4208;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 2; \r\nb = 0.5; \r\n\r\ny_correct = 0.5101;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = exp(1); \r\nb = 1; \r\n\r\ny_correct = 0.2569;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 0.5;\r\nb = 0.4;\r\n\r\ny_correct = 0.1252;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = sqrt(2);\r\nb = 0.1;\r\n\r\ny_correct = 1.1838;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":0,"created_by":487522,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-19T18:50:42.000Z","updated_at":"2026-02-05T14:11:12.000Z","published_at":"2021-02-19T18:51:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eArea between curves - Problem 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the area enclosed by the curves \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x) = sin(ax)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg(x) = bx\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for different \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e  and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e coefficients\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":50499,"title":"Find the area between curves (P2)","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 612.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 306.25px; transform-origin: 407px 306.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20px; border-block-end-color: rgb(60, 60, 60); border-block-start-color: rgb(60, 60, 60); border-bottom-color: rgb(60, 60, 60); border-inline-end-color: rgb(60, 60, 60); border-inline-start-color: rgb(60, 60, 60); border-left-color: rgb(60, 60, 60); border-right-color: rgb(60, 60, 60); border-top-color: rgb(60, 60, 60); caret-color: rgb(60, 60, 60); color: rgb(60, 60, 60); column-rule-color: rgb(60, 60, 60); font-family: Helvetica, Arial, sans-serif; font-size: 20px; font-weight: 700; line-height: 20px; margin-block-end: 5px; margin-block-start: 3px; margin-bottom: 5px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 3px; outline-color: rgb(60, 60, 60); perspective-origin: 384px 10px; text-align: left; text-decoration: none; text-decoration-color: rgb(60, 60, 60); transform-origin: 384px 10px; white-space: pre-wrap; margin-left: 4px; margin-top: 3px; margin-bottom: 5px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e Area between curves - Problem 2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 32.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 16.25px; text-align: left; transform-origin: 384px 16.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e Find the area enclosed by the curves \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"63.5\" height=\"20\" style=\"width: 63.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"68\" height=\"32\" style=\"width: 68px; height: 32px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; 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src=\"data:image/png;base64,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\" 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src=\"data:image/png;base64,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\" width=\"29.5\" height=\"19\" style=\"width: 29.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"76.5\" height=\"18\" style=\"width: 76.5px; height: 18px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = AreaCurves(a, n)\r\n  \r\nend","test_suite":"%%\r\nfiletext = fileread('AreaCurves.m');\r\nfor ii = [0.5, 0.6667, 1.3606, 2.7754, 22.3242]\r\n    assert(isempty(strfind(filetext, num2str(ii))),'Do NOT use provided answers in your solution')\r\nend\r\n\r\n%%\r\na = 1; \r\nn = 3;\r\n\r\ny_correct = 0.5;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 1; \r\nn = 5; \r\n\r\ny_correct = 0.6667;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 2; \r\nn = 2.5; \r\n\r\ny_correct = 1.3606;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = pi;\r\nn = 3.1;\r\n\r\ny_correct = 2.7754;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = exp(3);\r\nn = 12;\r\n\r\ny_correct = 22.3242;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":1,"created_by":487522,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-19T15:56:21.000Z","updated_at":"2025-08-25T11:22:08.000Z","published_at":"2021-02-19T15:59:16.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e Area between curves - Problem 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e Find the area enclosed by the curves \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x) = x^{n}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg(x) = ax^{\\\\frac{1}{n}}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e for different \\\"n\\\"  and \\\"a\\\" coefficients\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"420\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"560\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                       Plot of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and  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the area between curves (P4)","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 601px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 300.5px; transform-origin: 407px 300.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20px; border-block-end-color: rgb(60, 60, 60); border-block-start-color: rgb(60, 60, 60); border-bottom-color: rgb(60, 60, 60); border-inline-end-color: rgb(60, 60, 60); border-inline-start-color: rgb(60, 60, 60); border-left-color: rgb(60, 60, 60); border-right-color: rgb(60, 60, 60); border-top-color: rgb(60, 60, 60); caret-color: rgb(60, 60, 60); color: rgb(60, 60, 60); column-rule-color: rgb(60, 60, 60); font-family: Helvetica, Arial, sans-serif; font-size: 20px; font-weight: 700; line-height: 20px; margin-block-end: 5px; margin-block-start: 3px; margin-bottom: 5px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 3px; outline-color: rgb(60, 60, 60); perspective-origin: 384px 10px; text-align: left; text-decoration: none; text-decoration-color: rgb(60, 60, 60); transform-origin: 384px 10px; white-space: pre-wrap; margin-left: 4px; margin-top: 3px; margin-bottom: 5px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eArea between curves - Problem 4\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFind the area enclosed by the curves \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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\" 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style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"126\" height=\"18\" style=\"width: 126px; height: 18px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = AreaCurves(a, b, c)\r\n  \r\nend","test_suite":"%%\r\nfiletext = fileread('AreaCurves.m');\r\nfor ii = [6.5065, 6.3475, 0.1134, 9.4710, 4.0104]\r\n    assert(isempty(strfind(filetext, num2str(ii))),'Do NOT use provided answers in your solution')\r\nend\r\nassert(isempty(strfind(filetext, 'if')),'if: Forbidden')\r\nassert(isempty(strfind(filetext, 'switch')),'switch: Forbidden')\r\n%%\r\na = 1;\r\nb = 1;\r\nc = -2;\r\n\r\ny_correct = 6.5065;\r\nassert(abs(AreaCurves(a,b,c)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 1;\r\nb = 2.5;\r\nc = -5; \r\n\r\ny_correct = 6.3475;\r\nassert(abs(AreaCurves(a,b,c)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 0;\r\nb = 4.8;\r\nc = -0.5; \r\n\r\ny_correct = 0.1134;\r\nassert(abs(AreaCurves(a,b,c)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = pi;\r\nb = pi;\r\nc = -pi;\r\n\r\ny_correct = 9.4710;\r\nassert(abs(AreaCurves(a,b,c)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 2;\r\nb = 70;\r\nc = -6;\r\n\r\ny_correct = 4.0104;\r\nassert(abs(AreaCurves(a,b,c)-y_correct)\u003c1e-4)\r\n\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":487522,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-20T22:13:12.000Z","updated_at":"2026-01-18T15:37:37.000Z","published_at":"2021-02-20T22:13:59.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eArea between curves - Problem 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the area enclosed by the curves \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = y^4 - a\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = bx + c\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for different \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e coefficients\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc 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vertically even-degree polynomial's graph by its mean over an interval","description":"Let p be an even-degree polynomial with positive leading coefficient. Consider its vertical translation by shifting its graph by its average value over a specified interval [a, b], with a\u003cb.\r\nThe interval [a, b] is defined such that the endpoints a and b stand for the least and the greatest x-values of the equation p(x) = y_peak, the lowest and the largest real solutions, respectively. Here, y_peak stands for the highest local maximum of the polynomial p (see non-scale figures below). \r\nGiven p, return \r\nthe endpoints a and b if they exist. Otherwise, return a = '' and b = '' (see Hint 1);\r\nthe shifting constant, k, which stands for the above vertical translation (see Hint 2). Return k = '' if the interval is empty.\r\nHint 1. An n-degree polynomial has exactly n roots (counting multiplicity) in the complex number system. An odd-degree polynomial always has at least one real root. Therefore, a real polynomial of even degree always has at least one vertex, but might not have local maxima.\r\nHint 2. To calculate the mean of a continuous function, use the integral definition.\r\ninput: p\r\noutput: [a, b, k]\r\n ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 662.112px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 331.05px; transform-origin: 408px 331.056px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLet \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e be an even-degree polynomial with positive leading coefficient. Consider its vertical translation by shifting its graph by its average value over a specified interval \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[a, b], \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewith \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea\u0026lt;b\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe interval \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[a, b] \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eis defined such that the endpoints \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eb\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stand for the least and the greatest \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-values of the equation \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep(x) = y_peak\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the lowest and the largest real solutions, respectively. Here, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ey_peak\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the highest local maximum of the polynomial \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(see non-scale figures below). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, return \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 61.3125px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 30.65px; transform-origin: 391px 30.6562px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethe endpoints \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eb\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if they exist. Otherwise, return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea = ''\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eb = '' \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(see Hint 1);\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethe shifting constant, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ek\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which stands for the above vertical translation (see Hint 2). Return k = '' if the interval is empty.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint 1. An \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-degree polynomial has exactly \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e roots (counting multiplicity) in the complex number system. An odd-degree polynomial always has at least one real root. Therefore, a real polynomial of even degree always has at least one vertex, but might not have local maxima.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint 2. To calculate the mean of a continuous function, use the integral definition.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[a, b, k]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 264.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 132.4px; text-align: left; transform-origin: 384px 132.4px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"370\" height=\"259\" style=\"vertical-align: baseline;width: 370px;height: 259px\" 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LBIiFefy8/OLi4v7/vvv9+zZs3jx4sGDB/P7n8Viee+992xD3d69e3fo0IF/eZcuXdjKwo5Y5xF+ert27VhTDf/pN27cYAkxHTp0GDZsGP+qvn37Pvjgg3d88/DwcHboNxgM7MSwd+9e1iTAN2CeP3+eHbuDgoL4KWH8/PxYe4zJZPrll19EbztkyJDWVfbcuXOsGH379uWjyfbt23/11VcFBQVnz55lTWKRkZHnz59nLVXHjx9PSUl54YUXDh061IpP7NSpU2RkJBGVlZWxdzCbzXv27LFYLBzHPfHEEyqV/eF4rdvyvXr1at++Pf9UrVZv2rSpoKAgJyfHx8fnm2++Wbhw4YIFC5p6OcdxYWFhLOYgoh49erBNbTKZhF1jzJAhQ/g177//fhY/sRNtMxuEefTRR/kRcN7e3uy4TETnz5+vqqpq9UZrOT6rrKysLDY2lnXU/vjjj19//XUz+WQiAwcO9PPzY4/ZyYOIHnzwwfvvv5//FPagvLy8tra2trb2P//5D1vy8MMP81tPp9Oxl+Tn59+4cYPjuL///e8FBQWnT5/u1atXVlbW3/72t1mzZjXTltb8r9iuI0eOsH7M4cOH84UnQSBYUFBw7tw5IurVqxdrxCosLGQB69mzZ3Nzc9kWGDx4MBFdvnyZrdypU6fevXuzt+I4ju0/FouFtYcJifZVW67ZDs0T7uQajYbttM3v5G3fFBzHTZgwgQ3C2LdvX3V1Nd/1yXHc008/fe+99xIRa9QpKCj45z//WVBQsGHDhtjY2K1bt7aupnKDUcqu4OXlxdKjZs+eXVdXt3379qSkpMrKSnYtImq79vX1bfuRt9Wa//SysjJ29aBWq/njL3uV8GlTunXrNmzYsO3bt+fn5xsMhjFjxrDWZr4Bk4hqampY/w7LArZ9E/azF3508we4Zly4cIE9CAwMZL92uywWy5EjR5YtW3by5Mm23ycrIiJiw4YNJpNp3759zz33XFFREYtWu3Xr1kzI1bot37VrV9GSGzdufPjhh5999llL0mtEn6VSqdjhkohsJy1sS6aI6LX8U/4c0LqN1nL33XffvHnz5s+fzxIaWEctu9jt06ePXq/nO4xaWAv+R3TPPffw5zbef//7X7YB//vf/7IlfPK70K+//lpWVnbfffdVV1enp6d/+OGHohzMprTiGML/rPr06SMssI+PT2BgIAmaD1Uq1RNPPLFr1666urqMjIyRI0dmZWWx3enpp59mJ++amhrWwnHx4kW7m+7ixYu1tbXCH53tvmrLBduhea3YyR2yKfr169e/f/9jx4799NNPp0+f7tSpE4txg4ODhe+Zl5e3bNmynJwc11zWuhLaVJxlyZIlLPtar9cLT2+sHXLWrFns6R3TOzyJSqWKjo729vZm6WDHjx9n12QDBgz47W9/28I3EW0xb29v/vTpJHv37n3ppZdYT1BISMiSJUt27tzJkjZa4cEHHxw6dCgRHTt27Ny5c4cPH2btOnwHvwOJDqwmk2nevHlr1qwxmUxqtTo6Ojo1NXX16tWO/VBncMFGi4qK2rZt2+9//3sfHx/h8ry8vOnTpwuTeV2mtra2pqbGbDa//fbbSUlJV69e9fHxiYqKeu+99zZs2HC38zA5EN8f99NPP+Xm5rJUs7tKGOJjNd4dgwAZbgeHaMmm4LvOTSbTwYMHDx48ePnyZSIKDQ3lryVyc3NfeOGF/fv319fX63S6OXPm7Nmz55lnnnFJJZwObSrOMmLECJb/mJmZGRcXxzKbGIvF4qbTn7Rv316tVldWVpaXl1+5coXvMampqeGnnmve0KFDBw4ceOzYsZMnT3p5edXV1XEcFxMTwzebe3l5cRxnsVhCQ0NTUlLaPqajGT179mQPLl26xE7etuvU1tZ+8cUX7FJ74cKFL7/8MuuGv+eeVkb5fn5+v//97w8cOFBZWbl9+3Y2gMLb2zsiIsL24pvX9i1PRMePH2dZeDqdjiVLElEzw3MqKyuLior4LGyz2cwnsjj29HDlyhXhU7695ze/+Q0bL9a6jXa3+vTps3bt2rq6usLCwuzs7F27drFhxjdv3vzmm29YppQDcRzHX/GnpKSwHi5b+fn5LJsqICAgLS2NZR44/I4tfMdEXl4e61ZgT2/evFleXk7WjZedOnUaN25cXl7epUuXtm3bxpKHfve73/EJQ15eXqxqPXr0+Pe//22bqNcKfFaZU7eDwzlqU0RERHz88cfFxcU//vgja4BRq9VPPfUU/01t2bKFJTXHxMS888477IfT6sOU3HhINWTo4YcfZgnbly5deuWVVwwGAwucr1279tFHH6WmprLV7HZwONytW7cc8j733XcfO7tXVlay7C3m1KlTLRzJGRAQwI74Fy5cYLfG+O1vfytMvOjduzdLfCsoKOCHc5eWlrIZUwYNGnT06NGWF7j5IRu9e/dmVyTCzxJN/VJbW8vPVcDSaYno2rVrfM9RK0RERLB9Y/PmzSx04BOKm9L2LU9E169fZzthly5dWJM+EdlmnAh98803/AXf5cuXWcOSWq3u169fCz+0JfjcTCIym81ZWVns8cCBA/lW8VZstDviq7Z9+3Z+apba2to+ffrMnj37q6++SkhIEK3pQP7+/qyhiIiOHj3Kt7xu2LCB7X4JCQlms/nGjRssQAwMDGRbgIjOnz/v2ObYRx55hEXqhw8f5tOWiejQoUPnz58nov79+wu/9NGjR6vVaovFkpaWVlNTw3HcU089xQdePXr0YMkupaWlfL9SdXX19OnT7U4N0hKu2Q6Owh95HLUpHnjgAba3HDlyhPVLDhw4sG/fvvzH8VcsvXr1YmFKRUUF++48ACIVZ9FoNC+++CI7seXl5cXGxrJZeoYNG/b3v/+dXaP36dOnqQsph+jSpQu79jUajaWlpSaTqSVDRpuhVqsnTZrEKrV69WrW0pibm7t06dKWTyvCjx1gwsLChP2yGo2GDf24evVqYmJicXFxXV3d5s2bWaJ7aGhoS1J3+QvE3Nzc2traiooKux23Op2ODbm8evXqkiVLiouL6+vrs7Ozd+7cSUSdOnUaP378vffey1J9iWjr1q03btwoLS1NTk5mra+twx90Kisr2Z7AJxQ3xSFbng2CIKJTp04dPXrUbDbv3r1748aNzbxk9+7dH3zwQXV1dWlp6bvvvstmUmnht9ByrH+dBVIbNmzYs2cP3d7+/Dqt2Gh2qdVqFgoT0cmTJ81mc0VFxahRo9g1w6FDh1jvGBFdvHiRnRJYZrED6mlj/PjxLG38008/TU9Pr6+vLygoYN+Ij4/PpEmTVCpVu3btWP9mSUkJm1Hj2LFjK1ascGxJBg0axOp46dKlJUuWXLx4sb6+/uDBg8uWLaurq/Px8Zk5c6awIY3vj2OCg4NZLi0TEBAQHR3NcVxNTc3f/va3M2fO1NfXf/fddyzE7Nu3b0vyfkRcsx3ayPbI85vf/MYhm4LvOueXCKcRUqlUfDfQd999V1xcbDKZVq5caTtS0k0hUnEWjuPi4+NnzJjRVOu0RqNZvnw5f9B0hq5du7KxNlevXn3ssccGDRrU9u72p556asqUKURUVlYWHx8fHBw8ceLEurq6lleEn8uLbBowyXoempycnNGjR/ft23fFihVsErDExES+n6gZ/fv3Zz/pb7/9tn///hMnTmTtoiIqler1119nB+jDhw+PHj06ODh4xowZZWVlPj4+er2+T58+995779SpU1nuws6dO4cMGTJixIhdu3bxyTG2Y5HuSHTQUavVLelZaPuWHzJkCDssVlZWxsfH9+nTZ86cOTU1NawkFy9etB1sOXDgwFWrVg0YMIDVmoha/i203ODBg7du3frwww/37dv3f//3f9kcOWz78+u0bqPZxTdkrlmzpk+fPq+88oq3t/dbb72l0WgsFsv7778/aNAgNicpy9udMmUKm33L4Vi6ro+PT1VV1ZIlS4KDg9lAM47jFixYwH4FfDxdV1f35ptv9unTJyYm5vLly2xTXL9+vS1BM8/b2/uvf/0r+8TDhw+HhYUFBwfHxcUVFRX5+PgsXbpUtAX8/PxiYmL4X+64ceP4kXrM5MmT2e6al5c3YcKE4ODgP/7xjzdv3uzYseM777wjWrklXLMd2sjukcdRm4J1nbPHwkHvTExMDLsCPHbs2OjRowcNGpSWlubj48NfLbd9NICEEKk4kbe395IlS7788ssnn3ySD3h9fHz69++/ZMmSHTt28Ludk3Tq1Gn58uUPP/wwGxp9//3382MNWs3b2/svf/lLYmIiO0F27Njxf/7nfzZv3tzylFiVSsVHJ8IGTB6bh2b58uXsbov8p2zZsoVv9W3eqFGjkpKSWAm9vLzatWvXVGIQm3FL+Fnt27d/8sknt23bxg9Heuyxx9atW9evXz9256Z+/fqtXr16/fr17IJm7969tnM33RE/12dTG8FW27e8Wq1evXr19OnT2Yjc9u3bT548OTMzk52ELl26xE8zz3v11Vffe+89lmXl7+8/efLkTZs2tfBbaLlXXnll1apV/M01hw8fvnnzZn7781qx0ex67rnnXnvtNXZY9/Hx8fb2rqurGzhw4I4dO+bNm9ezZ0+2c/r7+w8fPnzt2rVvvfWW8FrWsaKior755puYmBiWBeLl5fXwww9//vnns2bNYsVQqVRvvPHGkiVLWIH9/f0fe+yxnTt3vvLKK0TEbhHgkJNQp06dUlNT165d+8gjj7DQnP8tvPTSS7ZXXMOGDWP7XkBAAD+wnMeCP+G7sf3n66+/bt1wLZdth7awe+Rx1KYICAhg7c1EFBoaKsolHzhw4GeffTZ8+HCW6tezZ8/ExMStW7eywog69dwOJ+FXazKZXn31VXY2FS6/du3atGnTbC9Vo6OjRWuCTJhMptmzZ7PzXDO5gcATbjG9Xv/SSy+1/X0cteWvXr363HPPselbZPVtOmqjAYB7kWzsT319/caNG3Nycthk3kIlJSVXrlzx9/fnJ+1hRE9BPtjMnkSkVqtb0a6rQIWFhex+PXc1ttOWora8ozYaALgXaSKV6urqFStWrFu3zm6LzpUrV8rLy5cuXTpjxgzXlw2at3DhQjbHeceOHdeuXTt48ODa2tqtW7eyESjsTqFSl1G+2IiA//73vykpKWzMQmhoaAu3mGK3fFs2GgB4AAkilby8vNdff/3kyZP9+/cvKCiwXeHs2bNEhCORPI0bN27Hjh03b94sKysTtYf5+/u/8sor7j4Rk1OdOXNm2rRp/LjKjh07zpgxo4U5EIrd8m3ZaADgAVydUWsymfR6fW5u7vz585OSkmwPNxaLJS8vr2PHjg6frxMcIjIyctu2bU8++WTnzp2F93mJiYnZunWrfHIa5Klr165s6icfH59HHnnkgw8+aHlKnWK3fFs2GgB4AFdn1JpMplWrVk2aNKlPnz4///zztGnTHn/8cWGerMlkmjlzZmlp6dixY7dv337p0iV/f/8JEybMmzfP4SMOAAAAQOZc3aaiVquXLl0qnCZB5Nq1axcvXiwsLPz0008HDBgwefLkzp07p6enR0dHs/kxAQAAQDlkd9+fiooKLy+vkSNHrlq1ig32qa+vT0lJWb58eXJyclM3gjEYDOx28AAAAOCORowYYXfSXtnN/BYSEnLgwIGNGzfyY5K9vLymTZs2ZMiQ3Nzcpu5icOjQIdtJq5TAYDCg4oqCiisNKq40Sq54Uy0OsmtTsSsgIECn0x07doy/jZmt0NBQ/nZiSoOKKw0qrjSouNIotuJ2ya5NhYiaupEem8vc9eUBAAAAqcguUlm+fPmgQYNSU1OFC0tLS3NzczF0GQAAQGlkF6lERESo1eotW7YUFhayJWxC27y8vLFjx7I7pQEAAIBCyC5PZejQoXPnzk1OTo6KihozZky7du1ycnKuXr06fPjwhIQElUp2BQYAAADnkd2Jn+O4WbNm9e3b97333svKyqqvr+/WrduSJUuef/55u+OTAQAAwINJGamEhITYncyN47iwsLCwsDDXF8ntPPHEE127dpW6FBJAxZUGFVcaVBx4sstTgbui2B0aFVcaVFxpUHHgIVIBAAAA+UKkAgAAAPKFSAUAAADkC5EKAAAAyBciFQAAAJAvRCoAAAAgX4hUAAAAQL4QqQAAAIB8yW42ffdmNFJEBE2fTomJUhfFHRiNDf9rtZSdTUR0C+uWLAAAIABJREFU4ULDwnvvpbNnrVbjH1ssd/1BaWmk1RIRabUNDwAAwE0gUnEoo5GMRtLrSa8nrRYhyx245s7YHCdewoKV8PCGB2FhFB7uipIAAMDdQ6TiUElJjY/5kCU8nMLDKS7OY6/mWXxmNNL06VIXpWVYI01amtVCPnwJCyOtFrELAChCRARlZze0NycmyvPQh0jFcYzGhi4Mkexsys5ubGXp2dNtzuhCfBdMdjbt39+whP3juWO9eHz4wiKYVvQxAQC4KXYwj4uTuhz2IVJxHK2WsrJo/37S6+2vwFpZiCg+viGAZVfwMoxh09IaUkbY+dtuBOYofAYJ/z970LOneJ3WYZtXFFQBAIDoAluuDf+IVByK7+hZv56MRnH/ghA7cbJdRIaX7/HxrviUwkJX/DCysqyesi0vbBZyahwGACBbwus3Gfd6I1JxAtbbR0SpqQ2NE021stDdhymsPSYsjJ1rfauriYj8/Khnz8aBM0TUrh2dPNnw2GikwsK7+xSLxU4iajNaF3BIEr/zrVlCwvAlO1sc3AAAeCThkVCuDSqESMXpWOpGYiIZjbR+fUPOSltYt9P4tum97h47zfNDZkjWYfhdEIYvrRuuxXENzWlunawDAEojw0Z9G4hUXIU1tLCzIOtxuHBB1v0ObBAvH45gJpJmsPYnFoYmJblx3jQAgPwgUpECGwRErb18dw30gLQOnzfNQhYPHp0OAOASiFTcjV5PRiN16EDXrxNRTXW1yttbpVLRvfdSbW3DOvypkQ2fwZlSEpgDEADAERCpuBvrE15NeTkRBQYGSlQaICKiwsLmkpD4kGXlSpo4EYEjAMBdwR0KAdqMJSFlZVFhYcOsxHYlJJBORzpdc8PXAQDAGiIVAMcRhSx2GY0UH++iex4BALg/RCoATsBCFouFCgvtDwK62xluAACUCpEKgDNptZSa2lwTCwAANAuRCoDz8U0sbCiQO0y1BAAgE4hUAFwoMRH9PgAAd0XKSMVkMsXFxS1cuND2T8XFxfPmzevXr19QUNCoUaM2bNhQV1fn+hICAACAtCSLVOrr6zdu3JiTk2P7p9OnT0dHR+/evXvo0KHR0dFms1mv1ycmJiJYAQAAUBppZn6rrq5esWLFunXrLDYd9nV1dR9++GFFRcWqVauioqKIqLKy8tVXX83IyIiKiho9erQU5QUAAABpSNCmkpeXFxsbu27duv79+/v6im8GXFBQYDAYQkNDw29PnxUQEJCQkODj47Nt2zbbyAbA83EcJSVJXQgAAGm4OlIxmUx6vT43N3f+/PlJSUne3t6iFc6cOVNWVjZs2DA/Pz9+oU6n02g0p06dun79umvLCyAPej3pdIhXAECBJGhTGThw4M6dO+fOnevj42P715KSEiLq16+fcKGPj09gYGBFRYXJZHJRKQFkguMaHhiNpNerQ0J8DQZJCwQAbi4igjiu4Z87XP+4OlJRq9VLly7t06dPUytcuHDBdqG/v3/Xrl1NJlNFRYUzSwcgd6qiIt+oKLc4uACATBmNjY/DwiQrRovJ7l7Kdgf4cBx3zz13CKqKioqKiopEC7t27eqwksmS2Wy2WCxms1nqgriagiqen6+aNUt8l2a9ntLSzB9/3OTdED2Ogr5xa6i41AVxNWdXXFVUJIxUzGYzuXwjs86TlpNdpGKbuUJEFovl1q1bzb/w0KFDsbGxooUrVqzo0qWLwwonPxUVFRzH1dTUSF0QV1NQxe+9lzZs8D10qMP8+SphLG40qh5/vDwhofJPf5KucK6joG/cGioudUFczdkVVxkMD/BPtNrLffvS5ctO+qxmvPDCC6IlRUVFCQkJdleWXaTSs2dP24VVVVUlJSVqtbp9+/ZNvTAmJqapSnqwgIAAIgoMDJS6IK6muIr36EGTJlFSkuj+QYErVwZu3UqpqR7fuKK4b/w2VFzqgria0yt+9mzjY622R48ezvqgZh04cEC0ZOXKlU2tLLvZ9Fmkcu7cOeHCmzdvlpeXt2/fXq1WS1QuABlITDT9/HNNaKjVQqORIiKQuQIALSLsSnaTKxzZRSq9e/e+//77DQZDdXU1v/D8+fNGo3HAgAEdOnSQsGwAkjNrNDW7dtm5MzMbxixKZwEAaIa9TgwZkl2kotFohgwZYjAYMjMz2TxvlZWVq1evvnXr1sSJEzl+xCaAkrE7HT7+uNVCNK4AQPOMRqvrGa1WqoLcFdnlqfj5+c2ZM+fYsWMLFiz4/PPPu3XrlpOTc/Xq1alTp4aKGr0BlEyrpW+/tc1cocREacoDAPInHJ+s1aL3p/WGDBmSnp4eFhb2008/ZWRkqFQqvV5vd0JbAKVjjSv84Qa3mwCAZuzfL3UJWkPKNpWQkJATJ07Y/ZNOp1u7dq2LywPglrRaysqy07gCACDihl0/JM82FQC4a4mJaFABgLvgJl0/hEgFAABAEUTptO4wjz6DSAUAAEAB3DOdlhCpAAAAKIIwndZ9klQIkQoAAIAiuOHstAwiFQAAAAUQ9v64T5IKIVIBUKi0NKlLAACuVVgodQlaCZEKgCLFx1NEhNSFAADXslga/qH3BwBkjd0/KzubdDqrBmEAAPlBpAKgMMLbfLKbGuIOzAAgY4hUABQmK8vqKYIVAJA3RCoAChMebnVTQyYigpKSpCkPAECzEKkAKA+7qaEoWNHrKT5emvIAADQNkQqAUmVl0fTpVkvS0jAgCADkBpEKgIKlpoqnWMjORrACALKCSAVA2VhPkBBGLwOAnCBSAVC88HAMCAIA2UKkAgC3BwQJGY0UH49gBQAkh0gFAIiISKsVj15mLSsAAJJCpAIAt9mOXrZYJCsMAAARIVIBADE+WEGYAgAyoJK6AAAgP6IEWwAA6aBNBQAAwENlZxPHWd2X1A0hUgEAAPBQ+/c3POA4902QR6QCAADgoYQTDYhu9eU+EKkAAAB4IqPRKlIJC5OsJG2DSAUAAMATie6JgTYVAAAAkBE+SYWItFrJitFmchylfO3atWnTpv3yyy+i5dHR0cuXL5ekSAAAAG7GI5JUSJ6RSklJyZUrV/z9/Tt06CBcLnoKAAAATRL2/sTFSVaMNpNjpHLlypXy8vKlS5fOmDFD6rIAwJ1wHKWm0vTpUpcDAASMRnGeituSY57K2bNniSgoKEjqggDAnbAZpeLjKS1N4pIAgJAwTNFq3br3R3aRisViycvL69ixo0ajkbosANAs4cSX8fFWneIAIC1PSaclGUYqVVVVly5dCggIyMjIGDVqVFBQUEhIyOLFi4uLi6UuGgBYS021ehoRgWAFQC48JZ2WZBipXLt27eLFi4WFhZ9++umAAQMmT57cuXPn9PT06OjoEydOSF06ABCYPl2cnoJgBUAOPGXON0Z2GbUVFRVeXl4jR45ctWoVG+xTX1+fkpKyfPny5OTklJQUtVpt94VbtmwxGAyiha+//nqXLl2cXmjp3Lhxg4iqq6ulLoiroeJSF+S2d94JqKxUb9nSuCQiovyrr6pHjHDs58iu4q6CiktdEFdzSMX9jh8PFDy93LcvXb7ctnI50pUrV5KTk0ULi4uLY2Ji7K4vu0glJCTkwIEDwiVeXl7Tpk3LzMzMzc09f/784MGD7b5wxIgRoaGhooW9e/d2VkHlob6+nogCAgKkLoiroeJSF0QgLY0iI+mVV/gFgc8+q9q+3bENznKsuEug4lIXxNUcUnGV8Lpdq5XbZgwICJg0aZJo4ZdfftnU+rKLVOwKCAjQ6XTHjh0rLS1tah2NRtNUOObBzGYzETXVzuTBUHGpC2Lt5Zdp82Zha7N63jxKTXVgsCLTijsfKi51QVzNMRU/dKjxcXi4DDej7fm6qKioqZVll6dCRCaTqba21nY5x3FeXl6uLw8A3FlWllVcYjRSfLxkhQFQOE+Z842RXaSyfPnyQYMGpVqPKSgtLc3NzcXQZQBZsw1WdDrJCgOgZIWFZLFIXQiHkV2kEhERoVart2zZUlhYyJZUV1evWLEiLy9v7NixOhz4AOTMNliJiJCsMAAKZ7GQxeLuQ5RJhnkqQ4cOnTt3bnJyclRU1JgxY9q1a5eTk3P16tXhw4cnJCSoVLIrMABYSU21mgUuO5siIigrS8oiAYA7k12bCsdxs2bNWrduXUhISFZWVkZGhkqlWrJkydq1azt16iR16QDgTrRaSk21mhOTBSsAAK0ixyYKjuPCwsLC3HymGgDl0mopK8sqSQVtKgDQWrJrUwEAT8CCFcaDMvsAwPUQqQCAc4SHU1YWwhQAaCNEKgDgNO4/6AAAJIdIBQAAAOQLkQoAAADIFyIVAAAAkC9EKgAAACBfiFQAAABAvhCpAAAAgHwhUgEAAAD5QqQCAAAA8oVIBQBkQHiTIABohYgI4jipC+EUiFQAQGocR0Yj7rcM0HpGI2VnExFxHHFcw2NPgUgFAKQjvArMzkawAtBKRqPVU8+6kQUiFQCQTmoqabWNT7OzKSlJssIAuK/9+xsfC39THgGRCgBIR6ulrCyrJXq9hzVcA7iC8FczfbpUpXASRCoAICnbYCUiAsEKwF3gk1SYsDDJSuIciFQAQGrh4aTXWy2Jj5emJAAeAL0/AACOl5hI06Y1PsVQIICWW7++8bFWi0gFAMA5Nm60GrCAoUAALSTs+vGsUT8MIhUAkA3boUBpaVKVBcBtCCOVuDjJiuE0iFQAQDa0WkpNtVoSH4/sWoDmiGZS8USIVABATsLDxUOB4uOVcCwGaCVhKK/VovcHAMD5REOBjEYMBQJokiid1hMhUgEA+UlMFGXX+kZFSVYYADkTtjh6YoMKIVIBAJnKyhIedmt27ZKuKAByZTRaRSoeN+cbg0gFAOSKz661WCQtB4BcCcMUD01SIdlGKsXFxfPmzevXr19QUNCoUaM2bNhQV1cndaEAwLXYRPsIUwCaIryjp4cmqZA8I5XTp09HR0fv3r176NCh0dHRZrNZr9cnJiYiWAFQHA+9RgRwPM/9saikLoBYXV3dhx9+WFFRsWrVqqioKCKqrKx89dVXMzIyoqKiRo8eLXUBAQAA5EE4pN9zZx6SXZtKQUGBwWAIDQ0Nvx0eBgQEJCQk+Pj4bNu2zYJ2YAAAAFue26Yiu0jlzJkzZWVlw4YN8/Pz4xfqdDqNRnPq1Knr169LWDYAAABwMdlFKiUlJUTUr18/4UIfH5/AwMCKigqTySRRuQAAAEACsstTuXDhgu1Cf3//rl27njp1qqKiwvVFajmjkdavp549afp0qYviJtgIO62WsrMbR9tduED33Uc//dS4gnBlxmxWq1RWey+f9s4esP979rRa4rmp8QAAHkt2kYrdAT4cx91zzx2afwwGg0ajES184oknHFayFvjlF5Ve70tESUk0fTqNHGkODa1x6ieyRibROVs+iopU7H/24MKFxmmKRPMV3T1xlVv4bnzUwrp0e/YkjcbpX5MDyfwbdx5UXOqCuBoqLnVBnKikpOTEiROihUVFRbYncUZ228Lb29t2ocViuXXrVvMvLC4u/vLLL0ULe/Xq1aVLF4cV7k7Wrg1gD4xGdt8SlUbjGxNj0mjqXnjB7IxPrKqqIiIvLy9nvHnLGY104UJDXFJe7vPLL17FxSo+QJEVPk4SpMmriNQajVmjMY8YUTNqVJ3ZbJbtTI8y+cZdDxWXuiCuhoq75uOiozsYDL4ajTkmxjRjRu3999/hVOsQ/v7+tufr4uJit4lUerL2emtVVVUlJSVqtbp9+/ZNvTAmJiYhIcGZRbsDo5G2bBEvLCpSrVwZSESLFpFWS9OnU1ycI/sgWN5xYGCgw96xaUYjabWUlkZEtH9/w5I2N43IBYurDAbflSuJbje9sF68xETpimXDld+4rKDiUhfE1VBx13ycry/R7VPVkCGuS134/PPPRUtWsoOvPTKNVM6dOxcZGckvvHnzZnl5efv27dVqtXRFuwOtlvR6ys5uckw7a2hh94hlUQsRhYXJa2SZsGtG2Fnj7IH6wuQSUcaJbeyq1ZLJZNJozOXlgaK5pFkIRYKKUKt6mtj67MvS6xt6i7RaBweaAAASsm5dlu/BTXaRSu/eve+//36DwRAXF8cPVD5//rzRaJwwYUKHDh2kLV7zEhMpMbEhrzYtrbmz4+3uoQYs2ZOFLGFhTsz95IvEn8Jd0DoiSmjVahvvotXqmpaXm4nI9qqjmbCPtQmx1F0+CGthBGY0NjQmsahl3Djq2lVebS1Kx3EUHW2nVRMAmuYudw2SXaSi0WiGDBly4MCBzMzMJ598kuO4ysrK1atX37p1a+LEiRzHSV3AO9NqG0IWIkpKaq6VhdfUWZOdxYOC6Le/bXxKRGFhDXtYTY2v2WzmW5r4gVM9ezaGIMKPcB5hOKLVUs+eDUvks+s3VR6+0ejChZZ+WR99RHQ7apk+XXYNY4rDDgsZGZSUhPgRoOX4RmiZk12k4ufnN2fOnGPHji1YsODzzz/v1q1bTk7O1atXp06dGhoaKnXp7hofsrCGlpacCIWEXRhN8G112VqHj0XodvMPySkcaQXblBQW1e3ff+fvi28bQ8giGeHVi16P7wCg5URtKrIlu0iFiIYMGZKenv7222/n5OQYDIZu3brp9frnn3/e7rAgd8E3tLA9Y/16IrLqAJIVPv7o3586d25Yopz5SPjOOGGUSc1+X6KQBeksrpOVRRERjU/j46mwULrSALgTYaQi5wif84w76bCcYWnH/rQa6/e528yJNhLljrDEEbanusUptry8nKQYF9CSqIVhIYvD+yKkqrjkmqt4UpLV9xEebnXbNjeHb1zqgriayypuNJJO1/g0K0viYKWZ87gc21SUhh8HJCQatMISUGw7g8xmM1nPESSMMzBPq8OxtjGiO6dO80O9wsMpLg7TFjtTYqJVR112NhJWAO6WnNtUEKnIlGi8blPKy02kyMsOORD26DUTsrBzKDt1Il5xltRUq8tDJKyAp+JbQtrcH+IuSSokwzsUArgdFrIUFlJhYcOAIFtGI8XHE8dRUpKHzJUnL1qtuMdHmLwC4DH4wwfHWaWT3z3hwB9EKgBKIQpZ7NLrSacjna5hghZwmPBw8UZHsAKex3HxhTAnUubtj4hUAByPD1mab2LR6SgpydVl82SJiVZHXNbrBuBJhPFF27qThe8k2zudMYhUAJzljk0sLOsW8YojZWVZxYbsDhcAnkE0OrQN8YWoDxq9PwBKJ2xisYV4xcFSU62eRkQgMwg8hONmvxe9EyIVACC6Ha9YLPa7hBCvOIxtwkp8vDQlAXAsxyWpuFE6LSFSAXA91r4i6qZg+HgFXRZtgoQV8EiOS4J1o3RaQqQCIJXw8IYUFrs3TYyIQLzSNqIZNzERHLg7xyWpkHXvj8zTaQmRCoC02DwgzcQr6LhoPRadWCxtnyMLQHoOTVJxr9wtRCoA0mPxit3+oLQ0JK+0Vng4YhTwHO+91/i4bakljot5XASRCoBcsP4g23xbJK8AAB092vg4Lq4t7+Re6bSESAVAbpoaz8w6g5555l4JygQA0hJ12ChmdloGkQqAHDUVr+zf79ehQyA6gwCUZf36xsdt7rBxr3RaQqQCIFv8fHG2ByXWGeReOXEA0HqOawZxu3RaQqQCIHMs2dZuZxAybQEUQTQ+uW1JKm6XTkuIVADcAj+5rQgybQE8n0ODC7dLpyVEKgBuJDGRdu2q0WjMwoUs0xaNKwAei423Z0Pu2xxcCC9sEKkAgOOFhtb8/LOpqcYVt+t+BoC7YLFQVpYD3w+RCgA4i91MW2SuAEDzHDojv+sgUgFwS01l2ur1NGWKBOUBAPkTNbu6RTotIVIBcGuscUXUhJuejjTbu8FxpNNJXQgAV3Dc7HEuhUgFwL1ptXbmiEOabUtxHNHt7QXg6dxx4A8hUgHwDImJdjLt9Hqcf5sl3DrZ2WiGAo8nbFNxl64fQqQC4DHYDQ5FR5/sbPQENS011eppRAS2FHgwN02nJUQqAJ7EbpoteoKaxLaXUHy8REUBcDp3nJ2WQaQC4GnQE3QXwsOtIjujEcEKeCphkop7kWOkcu3atfHjxwfZWLhwodRFA3APzfQEYXY4scREqy2VloY+IPBIjrvLoavJMVIpKSm5cuWKv7+/xlqHDh2kLhqA22imJwgnYjHbhBUEdODR3ChJhYhUUhfAjitXrpSXly9dunTGjBlSlwXAvSUmUliYVb8PC1ZSU2n6dMlKJTssrBNupvh4x05bDiAtUTqtGw1RJnm2qZw9e5aIgoKCpC4IgCew2xMUH498DGvh4VbbKDsbScjgSdw3nZZkGKlYLJa8vLyOHTtqNBqpywLgIViTgejYlJaGHFtrom2k16OfDDyGm875xsguUqmqqrp06VJAQEBGRsaoUaOCgoJCQkIWL15cXFwsddEA3Jtt2gpmWxFLTLR6inYn8BTum05LMoxUrl27dvHixcLCwk8//XTAgAGTJ0/u3Llzenp6dHT0iRMnpC4dgHuzHcDMhuUiWGkQHm6VXWs00tix0pUGlCo7mziu4Z+DCHt/3CudlmSYUVtRUeHl5TVy5MhVq1axwT719fUpKSnLly9PTk5OSUlRq9V2X7hly5YtW7aIFq5YsaJLly5OL7R0KioqOI6rrKyUuiCuhoq3+h169aIDB2jMmB78EpZj+89/lsfEyHd7uu4bf+yxTqGhvgZDw9PvvjMtXHg9IcHpn9sE7OpSF8TVKioqOqWk8E9rHn20ND29je9ZVKQyGh/gn/76a+nFizVtfM+2uHLlyoIFC0QLi4qKEpr4oXEWi8X5pWqrysrK6dOn5+fnb9y4cfDgwbYrrFy50m4lu3bt6pICSqa8vNxisShw/DYq3sb3KSpS2TalvPGGWdQ9JB8u/sZVwcHCi1BzXZ1rPtcWdnWpC+JqptzcwIce4p+a33hD3Gt797Kz6fHHGxomtFrKzze38Q3brqSkRLSEtTXYDVYka1MxmUyzZ8828BcuRKGhoU01mQQEBOh0umPHjpWWljb1hmzOFaeUVcZUKhX/v6Kg4m18H35YrjBYefttVXGxeG4RmXD1N56a2pBvbLGQpI3P2NWlLoir+VqfwlWRkdTmjfD9942PtVpZbNW7Ol/LLk+FiEwmU21tre1yjuO8vLxcXx4AT5WVRefPWy3BgKAGbJZ9d2hyBg/je+hQ4xMHjSd263RakjBSUavVmzZtKhDYtGmTWq1evnz5oEGDUq0v60pLS3NzczF0GcDhgoLEjSjZ2QhWiMhmHBCAawjDCgfNz+jW6bQkwzaViIgItVq9ZcuWwsJCtqS6unrFihV5eXljx47V6XTSFg/A80yfLh4QxEYvA4CriaaSdURYYTS6/c0hpO+sEhk6dOjcuXOTk5OjoqLGjBnTrl27nJycq1evDh8+PCEhQQ69awCeJzxcPJu80Ug6HaWmumVbMYC7Wr++8bGDun7cenZaRnZtKhzHzZo1a926dSEhIVlZWRkZGSqVasmSJWvXru3UqZPUpQPwWGzSfSFMtQLgak7o+nHr2WkZOTZRcBwXFhYW5o6daQDuTKulwkKr6IRNtWI7Ez8AOJ4Tun7I/dNpSYZtKgAgIa3WTo+PaDAzADiFE7p+iJwR/LgaIhUAsGL3doYIVgCczgmtH6JcWjft/UGkAgB2IFgBcClR109cnKPelafVIlIBAM+CYAXAdYQ/Lcd1/XhAOi0hUgGAZmRliccfIFgBcApRkoqDeEA6LSFSAYDmpaYiWAFwPsGPqub11x3yls4ZSyQBRCoAcAd2g5W0NEnKIjMcRxyHwA3aSrALmTWamtBQZ3wI2lQAwJPZBivx8YoPVjiu4QFamaCNwsPJYmF3xDQ77vZ2zulQkgAiFQBoEbvBinJP0KLRn/Hx0hQDPIzFUrNrl6PeTJSk674QqQBASyFnpZFWS3p941N26wEAuXLfrh9CpAIAdyU11eoETUoOVhITrQ7/aWlK3RAgRx6TTkuIVADgbiUmomXlttRUq6cREeJeIQCJeMAtlHmIVADgrqEbqAG79YAQ+oBAHjxjzjcGkQoAtAaClQbh4VaXq9nZlJQkWWEAbvOMOd8YRCoA0EoIVhqI7jug1ytyK4CMeFKSCiFSAYC2SE3FvYGIiCgx0eop+oBAUqJ0KbSpAICiZWXRxIlWS5Q4z0p4uFXCitFIERHSlQaUzpOSVAiRCgC03datVhdtCp1bBAkrIBseM+cbg0gFABxAlKphNJJOJ1lhJJOVZXVaQMIKyEBcnNQlaDNEKgDgGLbBihI7QEQzrCixcQkkJkqnRZsKAEAjUYJtdjY98YRkhZFGeLjVJL6FhZKVBJTKk+Z8YxCpAIDDaLXiNoVvv1VeywqbZf/2rXEBXMzD0mkJkQoAOJZWK25HUGJqqWjiWgAhlsbFcU56e0+a841BpAIADmY7xbxeT2lp0hQGQHaMxoYeGo4jjnNs2rWHzfnGIFIBAMcTTS9CypxkBcAuYRujaHB7m3nYnG8MIhUAcArbYEWh09cCCIkaPRw9htjzklQIkQoAOI9oHAwRRUSIr/kAlEU0gFh06yxHv71nkDJSMZlMcXFxCxcutP1TcXHxvHnz+vXrFxQUNGrUqA0bNtTV1bm+hADQRomJdu5iCKBc69c3PnZy34wHzPnGSBap1NfXb9y4MScnx/ZPp0+fjo6O3r1799ChQ6Ojo81ms16vT0xMRLAC4I5Ek6wodEY4ACLKznZq14/nzfnGNEQq1dXVeXl5LgsFqqur33333eXLl1ts5huoq6v78MMPKyoqVq1atWnTpuXLl3/33XejRo3KyMgwGAyuKR4AOFZWllV0kp2NYAUUSdig4oRJ2TxvzjemIVKprKycNWvW0KFDFy1adOzYsfr6eud9ZF5eXmxs7Lp16/r37+/r6yv6a0FBgcFgCA0NDb+9jQMCAhISEnx8fLZt22Yb2QCAW9i3Tzx9LSaaB2UxGq0G6zs6Q4U8NJ2W+Ei83z6eAAAgAElEQVTF19d30KBBdXV1W7ZsiYmJeeihh/72t78VFhY6PDIwmUx6vT43N3f+/PlJSUne3t6iFc6cOVNWVjZs2DA/Pz9+oU6n02g0p06dun79umPLAwAuI5q+Ni0Nk6yAkog6ZpyQReJ5c74xDZFKu3btVq9e/fPPP69fv/73v//9zZs309LSHnvssUcfffQf//hHUVGRA0OWgQMH7ty5c+7cuT4+PrZ/LSkpIaJ+/foJF/r4+AQGBlZUVJhMJkcVAwBczHZGOKVPsoI+MEURdf04utHDI+d8Y6wyar29vUePHr127VoWskyYMKG8vPz9998fM2ZMZGTkxx9/XFpa2sbPU6vVS5cu7dOnT1MrXLhwwXahv79/165dTSZTRUVFGwsAABLCJCuN2OSkCq288ojiiMREZ3yCkCe1qajsLmUhy+jRo+vq6nJzc7/88susrKxly5a9++67vXr1mj179rhx49RqtTMKZDerl+O4e+65wzAlu/m2TzzxRNeuXR1TMlkqLy+XugjSQMXd15Ah9Kc/qf7xj8YDSHw8bd9u0mjMzbzKAyouFNihQ8OjiIiaXbtqQkObWtPDKt5yHlZx348+4rMyzRqNacgQaqKCra747t2+RA0fotGYy8vl2wVRUlKyZ88e0UKWomp3/Tuc/q9evXrkyJFjx46x1hSLxXLu3Lk///nPjz766Mcff+yMsUK2mSvsc2/dutWKd/PsMAXATb35plmYTWg00qxZ9q+aPJKv9WWVatYsqUoCLmI0qj77rPGpc5o7vv++8Uf0wgvNxf2Su9tTs52jg8ViKS4u3rx581dffXXp0iUi4jhu4MCBcXFxjz/+OBHt2bPnn//857vvvltVVfXHP/7R7vtmZmbOnj1buCQlJSUyMvKOBerZs6ftwqqqqpKSErVa3b59+6ZeGBoampCQcMf390iBgYFSF0EaqLj7Sk21ag43GHyffdb3jncg9oCKExGNG0d6PT99r6qoKPDZZ5u//bKHVPzueUjFy8upqIh/ppox4471utuKG40knJ5s3DjfwEDx0FpZuavzdWObisViKSwsTE5OfvTRR8eMGfP+++9funRJp9MtWbLkP//5z9atW6OjowMCAgICAiZNmrRixQp/f/9vv/3W4aVnkcq5c+eEC2/evFleXt6+fXsndTkBgOtlZYnHLQtv3ObhEhPFlUfCigdbtqzxsaNvSciIklQ8aYgy8W0qpaWlcXFxv/zyC3varVu32NjYp59+unv37nZfptPpOnToUFtb29T7RkZGFhQUtKJAvXv3vv/++w0GQ1xcHD9Q+fz580ajccKECR34zl0AcH+pqaTTNT7V6ykszKMyAZsjqnxEhDh2A4+xZw9xXMNj50xxL5pJxcMilYY2FYvFUlVV1bFjx5kzZx44cODgwYNz5sxpKkwhorq6uueff/7tt992eIE0Gs2QIUMMBkNmZiYbGl1ZWbl69epbt25NnDiR479sAHB/tuOWFTQUyO6gbfBUFgtZLM64JSHjqTOpMA1tKgEBAZ999tkDDzzg5eXVkpd179795ZdfdkaB/Pz85syZc+zYsQULFnz++efdunXLycm5evXq1KlTm8oKBgD3xcYtCycWiYigwkJPuyi0j91smr/fNLsl0h2zdcB9FRY66Y2deTch6TW0qfj5+Wk0mhaGKc42ZMiQ9PT0sLCwn376KSMjQ6VS6fV6uxPaAoAHYOdrIQXNiGabsKKgbB1wDM9OUqGm5lNxjZCQkBMnTtj9k06nW7t2rYvLAwBSSUykkycpI6PhqbIaFxSdrQMOIJqm3/MilTvMpwIA4Bpbtii1ccFuto7oMhmgaaJp+j0PIhUAkAvRLQz1esVk19p2gDknERA8kjCsdcI0/dJDpAIAcqHooUCihJU9ezAUCFrCaPT8BjhEKgAgI7aNCwo6X4vmU0lLU0yYBq0nDFO0Ws9McEKkAgDyImpcYNm1SiHsALNYPPO0Aw4lTOfyyCQVQqQCADJkO9H+//6vMm5hyHeAWSxSFwXcj6dGtohUAECOUlOtLhD/8Q+1wSDrO645THg4whRoIeFtPokoLEyykjgVIhUAkCOtVjwUKCrKF2kbAEJKSFIhRCoAIFtson0hBWXXArSA6MaEngqRCgDIV3i41Q3dlJVdC3Annn1jQh4iFQCQtdRUpc5dC+7IhaG0QpJUCJEKAMifKLtWQXPXgnthsQPHEce55tN4HpykQohUAED+tFr68MMa4RIFzV0LbkSYSCW866RzKCRJhRCpAIBbCA2t+eqrcuESZNeCvIg6Y4QJVs6hkCQVQqQCAO4iPJymTWt8iuxakBfRZLFOvlWgKC6Ki3Pqp0kMkQoAuI2NG5FdC7JkNFJaWuNT5zdxiJJU0PsDACAXoungkF0LsiBqUBHtpk6gnCQVQqQCAO6FvzEOLyLC8+96bx/HoQNMFlzeoEJKSlIhRCoA4HbCw0mvt1qiuOxana5hHCw6wOTAtRkqpKSZVBhEKgDgfhITxQkrb74pWWFczWi0akRCB5jkRA0qzu+MUc5MKgwiFQBwS1lZVgfot99WzPnabgeYUiovP8IGPZc0qJBNI47HQ6QCAO5KlLaooPO17c0bFVR5ORFlqMyZ45rAQdim4vENKoRIBQDcl23jgoISVpCtIweiBpXnnnPBZ4p6/zw+SYUQqQCAWwsPt7qmVNZ0cKJsHaORIiMlK4wCZWeLR+C4pEFl/frGx0pIUiFEKgDg7kQJK6LTh4cTVX7vXiVFalJz+RwqjHD3VkKSCiFSAQAPoNyEFbKpPMYtu0ZamtVO5pJEWrIZn+yqj5UYIhUAcHuKTljRaqmw0GqJXm+V5gnOILwBoVbrgvsRMqJJDtGm4nQmkykuLm7hwoWi5deuXRs/fnyQDds1AQAYUYKpshJW7EZqCmpWkojFQhYLkU2zljOJJtFHpOJc9fX1GzduzMnJsf1TSUnJlStX/P39NdY6dOjg+nICgLuwnQ5OQd0gGLcsFYvFlUmtwq/UVe040lNJ8qnV1dUrVqxYt26dhQWk1q5cuVJeXr506dIZM2a4vmwA4L5SU0mna3yq11NYmCIGRxDdblYStixFRJC9Yyy4KaVNos+ToE0lLy8vNjZ23bp1/fv39/X1tV3h7NmzRBQUFOTyogGAe1N0wgoRJSZaXWiLJlwBN6e0SfR5ro5UTCaTXq/Pzc2dP39+UlKSt7e3aAWLxZKXl9exY0eNRuPisgGAB1B0wgoRpaY2nMEKC5UyMkQxREkqyiFBm8rAgQN37tw5d+5cHx8f279WVVVdunQpICAgIyNj1KhRQUFBISEhixcvLi4udn1RAcAdKTphhYiysqiwUFmnMmUQzTOnHK6OVNRq9dKlS/v06dPUCteuXbt48WJhYeGnn346YMCAyZMnd+7cOT09PTo6+sSJE64sKgC4L9FoDMXdbxhhisdRbJIKSZVR24yKigovL6+RI0euWrWKDfapr69PSUlZvnx5cnJySkqKWq22+8KioqKioiLRwq5duzq9xJIym80Wi8VsNktdEFdDxaUuiKvdbcU1GvruO3r88cZDXHw85ee733bDNy51QVytqYobjY07s0ZjHjWK3HfblJSU3NX6sotUQkJCDhw4IFzi5eU1bdq0zMzM3Nzc8+fPDx482O4LDx06FBsbK1q4YsWKLl26OKusMlBRUcFxXE1NjdQFcTVUXOqCuForKt63LyUkBKxcGcieGo00erQ5Pb3UOQV0FnzjUhfE1Zqq+MGDvyHqyB5rtXT58mWXF82RXnjhBdGSoqKihIQEuys7K1LJzMycPXu2cElKSkpka++eFRAQoNPpjh07Vlra5FEmJiamqUp6sICAACIKDAyUuiCuhopLXRBXa13F//UvKiig7dsbnhoMvuvW9XCvNFN841IXxNWaqvi+fY2P33pL1aNHD1eWyuFETRJEtHLlyqZWluNs+iaTqba21nY5x3FeXl6uLw8AuK9Vq6yeKi5hBTyCKElFaZwVqURGRhZYa2GDyvLlywcNGpRqnQ5XWlqam5uLocsAcLeUPsMKeIT16xsfK2omFUZ2bSoRERFqtXrLli2Ft++5xSa0zcvLGzt2rE44/SQAQAsofYYVaDXR/QClo9jxyYzsIpWhQ4fOnTu3oKAgKipq9uzZCxcujIiI2Lx58/DhwxMSElQq2aUAA4D8KX2GFWid9euJ40jqK2RR109cnGQlkYrsIhWO42bNmrVu3bqQkJCsrKyMjAyVSrVkyZK1a9d26tRJ6tIBgLtS+gwrTXGvBGNXys5uaIszGonjJCyIYifR50nZRBESEmJ3MjeO48LCwsIUNa8NADgZS1gR9vvEx9PtTmalYifg//s/cRwHRqNVQpNWS9nZUsUIoiQVBZJdmwoAgJMgYcUK306QlqbsDWGDhSnCpozp0yVsyhAWRIENKoRIBQAUxTZhRaF9QKJqZ2cjWGm0fr3V9pk+XcI+MiVPos9DpAIAyiLq6IiIUGSwEh4uHr2NYIXh01MYrVbarjGFj09mEKkAgLJghpUGdoMVqce5SMw2PUXqDB6Fj09mEKkAgOLYJqwgWGlgNJJOp8hWJiKjkf7nf+STnkIYn3wbIhUAUCJRwkpamkLPzhQeLh4BxQI3BW6O9evp228bn4aHSz6EG+OTGUQqAKBQtgkrspmS1LW0WiostBr/yoZFKSpYSUqSVXoKg/HJDCIVAFAoJKw0YsGK6Jo9IkIpU/mmpdkJU2QQGmB8MoNIBQCUKzwcs+wLZGWJz4d6veeHb2lpdrJoZRAXYHwyD5EKACia6Oys9Fn2s7Jo+nSrJZ49L5xtNrXUWbQ8jE/mIVIBAKUT5U16fCPCHaSmilM0PDh2E3Xx6PWSZ9HyMD6Zh0gFAJQOs+yLTZ9ulcJjsUhXFOfjayfpXLQiGJ8shEgFAMDOLPuKTlih26OXtVoPD1MYi4XCw+Uw2McuhXf9ECIVAAAmK8uqK0DpCStkb3CUB5NZTUU5vgqHSAUAoIHoolrpCSuEk6Q00PUjgkgFAKCBbcLKM89IVhhQLNEMhAgXEakAADQSJaxs3ar4PiBwOdGoH4UnqRAiFQAAEdtZ9hGsgCsdOuTLP0aYQohUAABEbBNJlT4OCFzIYPA1GBojFSVPTctDpAIAIBYebjVTa3Y2smtbDGFd2wgbVDA+mUGkAgBgh+jeL2lp6ANqAY4jvZ50OkpLk7gkbnsTAOFuJrqxgWIhUgEAsM82YUU0KAOscFzDA3YzHZ1OmvYVNsdwfLw7hpa4K6FdiFQAAOxjd9UVQh/QXTAaG9pXXBavGI2UlEQ6XePZng+e3ATuSmgXIhUAgCaJbqybnS19t4Z8FRbaObWyeIXjKCnJWduONUSwVhzhfDhuCHcltAuRCgBAc0Sz7Ltnr4JLsEFTWVn2z7F6fWOXkKO2IGtEiYigiAg7YZBtm5i8YWrapqikLgAAgNylplplZ8bHU2GhdKWROTZVGYshbKMH1sRCRFptK+8rxM7n+/eLT+xCWq2sbozcQsLaoOtHCG0qAAB3YDvLvnsOK3Eh1p5RWNhkd0wzcUZTWA6KTkfx8U2OxdJqSa+nwkK3C1PIJkkFeIhUAADuTDTLfnY2+oBaQKulxMSGeKXtTQSJic0NvnLnGIVsIjf3rISzSBCp3LhxIzk5+ZFHHgkKCurXr9+UKVMOHz5ssViE6xQXF8+bN69fv35BQUGjRo3asGFDXV2d64sKAMDDLPutxOKVrKyGkMWxzQWso4e9uTuf3oUxGLp+RFwdqRQXF8fExKxZs6Zdu3aTJ08eOnToTz/99NJLL+3evZtf5/Tp09HR0bt37x46dGh0dLTZbNbr9YmJiQhWAEBCtmkVGLR8d/gmlsJCSk0l6wvUu3sf1iHHAhTRJH3uSTiUG10/Ii7NqLVYLJ988klBQcGiRYtmz57t5eVFREePHn355ZffeeedgQMH9ujRo66u7sMPP6yoqFi1alVUVBQRVVZWvvrqqxkZGVFRUaNHj3ZlgQEAhNj5kU+9YDOcudX4EnlgDSGtkJrqqQ0Owva511+vIfJtclXlcWmbyq+//rp///7g4OBJkyaxMIWIHn744SeffLK4uPjs2bNEVFBQYDAYQkNDw2/viwEBAQkJCT4+Ptu2bbO0OgYHAHAEUcIKZtl3KdH8Np5CuAtpNObQ0BrJiiJLro5U7rnnnuDg4A4dOgiXd+zYkX985syZsrKyYcOG+fn58Qt1Op1Gozl16tT169ddV1wAAHswyz44lrDrR6MxS1cQmXJppNK/f//vvvtu9erVKlVjr1NlZWVWVlZAQECXLl2IqKSkhIj69esnfKGPj09gYGBFRYXJZHJlgQEAbCFhBRxINOpnyhQ0qIhJPErZYrF8/vnnx48fHzNmDItOLly4YLuav79/165dTSZTRUWFy8sIACDGpjfjZWdLczM+8ACiUT+4f7ItKeeotVgsW7ZsWbFiRVBQ0OLFi729vYnI7gAfjuPuuecOQdWWLVsMBoNo4euvv86aajzVjRs3iKi6ulrqgrgaKi51QVxNhhXftImiozsYDA2Zj3o9DR5cPmKEg0sow4q7hnIq/pe/dOLPxV271ly5coU8veJXrlxJTk4WLWRDg+2uL1mkUl9f/8knn/z973//7W9/+8EHH3Tv3p0tZ/GKiMViuXXrVvNvOGLEiNDQUNHC3r17O6S0slVfX09EAQEBUhfE1VBxqQviavKseGIiRUU1Pp03T33mjIMPqvKsuAsopOJGI+XkNO4ziYnk7+9Pnl7xgICASZMmiRZ++eWXTa3vrEglMzNz9uzZwiUpKSmRkZHssclkSkpKysjIGDRo0Pvvv9+tWzd+tZ49e9q+W1VVVUlJiVqtbt++fVOfqNFomgrHPJjZbCYitVotdUFcDRWXuiCuJs+KjxtnNWi5qEj11FPqVtzKphnyrLgLKKTi//lP42OtlsaN8y0vV5MCKm57vi4qKmpqZQnyVEpLS2fOnLlly5Zx48atW7dOGKbQ7Ujl3LlzwoU3b94sLy9v3769x395AOBebGfZR8IKtBzu9dMSzmpTiYyMLCgosF1eWVn5pz/96ciRIzNnzly0aJFtX0/v3r3vv/9+g8EQFxfHD1Q+f/680WicMGGCaHgzAIDksrKI4xqf6vUUFuaRs36Ag/3/9u49Lubs/wP4GRW1TSJautiaScqSculiNypCiSIkt1WotUuIrNj9UtaPjdZlQykq1veLbcuuuxUVxShWyK5cKqtpu1A0k6Kp+f3x2R3TTNl1mc9nmnk9H/vYR/OZM595fzTNvOec9zkHe/38S7T2qTQ2Nm7YsCEnJycsLGzFihWtlqSYmpra2dnxeLz09HRqnTeBQBATE9Pc3Ozt7c2Sfj8AAFAOmLQMb0A6TVHRpXffDVoram/cuHHs2DFCyN69ew8cOCBz7/r1652dnXV0dD7//PNr164tXbr0wIEDxsbG2dnZlZWV/v7+8gWzAADKwNWVnD1LRo7862ZJCXFzk01fAGRID/0gTXkFWjOVvLw8aum2yspK+XsbGv5a7sbOzu6HH374v//7v+zsbB6PZ2xsHBERMW3atFb7YAAAlMGIEcTV9eW35MxMkpmJjx9ok8zQz+zZjEWi/GjNVObPnz9//vx/05LD4ezevVvR8QAAvENJSYTDeXmT6lZBsgKtkqmlxevkFRheoxYAQGXIr7KPeUDQFukOFaQpr4ZMBQDgnXF1bbEaemYmqmuhFRj6eS3IVAAA3qWkpBZfkZOTW3wmARAM/bwmZCoAAO9YUlKLm25uLXahA5BOXrEl4T9CpgIA8I7JF6xgDAgkqHlhEi4ujEXSXiBTAQB491xdyZIlL29ilX2QkH4lYOjn30CmAgCgEFu2tPgQiohAwQpgBf03gUwFAEBRZD6HULACMivoo0jl30CmAgCgKK6ustW1KFhRc9g8+Q0gUwEAUKCAgBZjQChYUWcY+nkzyFQAABRLZk19FKyoLdTSvhlkKgAACoeCFSgpIcnJL2+iQuXfQ6YCAKBwKFgBmdwUy6j8e8hUAADoEBBAJk58eRMFK+pG+tft6oqhn9eATAUAgCZpaShYUVOopX0byFQAAOiDghX1hC0J3wYyFQAA+qBgRT1Jd6ggTXldyFQAAGiFFVbUjcyWhLNnMxZJO4VMBQCAbvIrrGAMSIVt3/7yZwz9vAFkKgAADJApWOFwUF2rmkpKSGrqy5uopX0DyFQAABjg6koyMlocQcGKSpKppcWCb28AmQoAADNkFtUoKSFubowFA4ogsy4txn3eDDIVAADGyBSsyJReQnuXmdmiAgm1tG8GmQoAAJNkJi27uSFZUR3SQz9Yl/aNIVMBAGCSuTkKVlSTTA8ZamnfGDIVAACGubqSiIiXN1Gwohqkl8nB5OS3gUwFAIB5a9ZgOTiVIrPRD6b8vA0GMpXa2tqoqCh7e3sul2ttbT116tTc3FyxWCxpUF1dPXbsWK6csLAw+qMFAKCHTMEK9i9s12QmJ2Po523Qnanw+fxJkybt2rWrc+fOfn5+gwYN+vXXXz/55JNTp05J2pSXl1dUVOjq6pq21LVrV5qjBQCgjXzBCqpr2ylMTn63NOl8MrFYvGfPnqKiouXLlwcHB2toaBBCrl69On/+/PXr1/fv379Xr16EkIqKiidPnqxatWru3Ll0hgcAwCyqYEW6ZiUkhH3zppCxgOCNYHLyu0Vrn8qjR4+ysrIsLS0nT55MpSmEkMGDB48bN47P5xcWFlJHqB+4XC6dsQEAKAOZgpXSUs2JE7swFg28EUxOfrfozlQ6dOhgaWkpM47TrVs3yc9isfjOnTvdunUzNTWlMzYAACUhvxwcqmvbEUxOfudoHf3p27fvmTNnZA4KBIKMjAw9Pb0ePXoQQurq6srKyvT09NLS0o4ePVpWVqarq+vl5RUSEmJiYkJntAAATElKIhzOy5sREcTFBV/N24etW1/+jMnJ7wTDs5TFYvGBAwfy8/OHDx9ubW1NCKmurn748GFxcfH+/fv79evn5+f3/vvv//DDD76+vtevX2c2WgAAerRaXStd+gDKqaSE/Pzzy5voUHknaO1TkSEWi1NTUzdv3szlcsPDw7W0tAghT58+1dDQ+Pjjj7/77jtqkKipqSk+Pj46OjoqKio+Pp7NZrd6Nh6PJz9gNGbMGEVfBbOEQiEhRFOTyd8jI3DhTAdCNzW88CFDyIoVmlFR2pIjgYHk6FF1qa5tp7/xwMCXn1CmpqLJkxuEr/kba6cX/lrKy8vlux5KS0vbqvpg7N+iqalpz549mzZt+uCDD3bu3CkZ2bGxsTl//rx0Sw0NjZkzZ6anpxcUFNy/f9/W1rbVE/L5/B9//FHmoIWFBTWopKrq6uoIIZLyZPWBC2c6ELqp54UvXkyuXev2yy8dqZuZmWTUKM20tBpmo6JHe/yNl5SQzMyXmcrHH4sEAsHrnqQ9Xvjr0tXVlf+85vP5dGcq6enpwcHB0kfi4+Pd3d2pn4VCYWRkZFpa2oABA3bs2GFsbPzqs+np6XE4nGvXrlVVVbXVZtKkSYsXL377yNsXHR0dQkiXLmo3NQAXznQgdFPbCz906ImnZzOP91fPCo+nHR9vpA5jCu3xN75q1cufzc3JwYPahBi97kna44W/gQMHDsgc2bZtW1uNGahTqaqqmjdvXmpqqoeHR2JionyaIhQKnz9/Lv9AFoul2mkmAIC82NgG6ZtYu1Y5YbU3xVFUpuLu7l7UEtWhIhAIli1blpeXN2/evK1bt8ovOxsdHT1gwICklstKV1VVFRQUYOoyAKghrF3bLsjsR6gO/V60obVPpbGxccOGDTk5OWFhYStWrKBKaGW4ubmx2ezU1NTi4mLqSH19/ebNm+/cuTN69GiO9Lw9AAD1ILPZMiEkMJCZSKBV8h0q5uZMxaKCaK2ovXHjxrFjxwghe/fulR+jWr9+vbOz86BBgxYuXBgVFeXp6Tl8+PDOnTtnZ2dXVlY6ODgsXrxYtcuhAQDasmZNiyXFSkrIiBHk3DkmQwIJdKgoFK0f/Hl5edT8q8rKSvl7GxoaCCEsFisoKMjKymr79u0ZGRlNTU3GxsYrV66cNm1aW/OTAQDUQUZGi3Ef6qbMwBDQDx0qikZrpjJ//vz58+f/YzMWi+Xi4uLi4kJDSAAA7YjM2rWZmSQ5mQQEMBYPkJa7/JibYz/Cd4/hNWoBAODfk6+uDQxEdS2TSkpalBBhP0JFQKYCANCeuLpiKpASQYcKDZCpAAC0M5gKpCRkOlTGj0eHikIgUwEAaH/WrGnxoVhSQtzcGAtGbclM+fH1ZS4UlYZMBQCgXcrIaJGsZGYSb2/GglFD8lN+0KGiIMhUAADaK5lk5ehRDAPRR/qfGmuoKBQyFQCAdqzl1iMkObnFF31QEOlV+AghAQFYQ0WBkKkAALRjmLdMv5ISLEpLK2QqAADtG+Yt00ymQwVpiqIhUwEAaPfk5y0jWVEQ+Q4VrBGsaMhUAABUwZo1sh+ZqK5VhMxMUlLy8qZMnRAoAjIVAAAVkZQku8iK9CZB8PZKSlrkf5iZTA9kKgAAqkNm3jJWhHu3UEjLCFr3UlYqPB7v8uXLTEfxthoaGggh2traTAdCN8Yv3NHR0cnJialnB3iFjIwWRSqZmcTNTbbkFt4AtXO1RHQ0OlRoor59KpcvX+bxeExH8ba0tbXVME0hTF+4aqS5oMJkiieoZAXehsy4j7k5GTyYuWjUjPr2qRBCnJycFi9ezHQUAADvmLk5KS5uUaSCnpW3tHdvi0LaNWuw1Bt91LdPBQBAhcmvCJeZidlAb0hmz2RXV8xMphUyFQAA1SS/IlxyMpKV1yY/7oOZyTRDpgIAoLKQrLw9bPHDOGQqKisuLo4rZ+DAgeHh4Xw+n+nolIJQKJw+fbqLi0tlZSXTsQAoSqvJivRsW3gF+Q4VzEymn1pX1BfvBXIAACAASURBVKqDYcOGmZiYSG7eunUrJSXl6tWrycnJ0sdpU1lZmZSUNH78+A8//JD+ZwdQT1SyIj39JyKCmJmh2OKfzZ378meM+zAFmYqKmzVrlru7u+SmWCyOi4vbtGlTSkrKkiVL6I8nLS3tf//739ixY+l/agB15upKkpJadA9QPyNZeYXISHLu3MubWJGWKRj9US8sFsvd3b179+6//vprXV0d0+EAAH0CAmS7BAIDWyxlBtJk5vugQ4VByFTUjr6+vo6OjkgkEovFhBA+nx8eHu7g4MDlci0sLNzc3Pbt29fY2Ej+LuNYtmxZYmKitbW1jY3NkSNHqONRUVH29vZcLtfGxmbt2rW1tbXUydPT07lc7tGjR7du3Uo1cHZ2PnLkSFNTEyEkLCxs48aNAoHAx8dn+vTpQqFQPjzq5AMGDOByuR4eHr/88ou/vz/VuNV4mpqajh8/7uXlZW1tTcUTFBRUXFwsHc+RI0fWrl1rbW1tYWExceLEvLw8mSctLCz09/e3tLS0trYOCQlBHQ+oqlaTFdSsyJPZhQBpCrMw+qN27t27V1VV5eDgoKurW1ZWNnfu3EePHk2ZMqV///4PHjw4dOhQZGRkp06dpk6dSrVPT0+/cePG6tWrKyoqbGxsBALBggULcnJynJ2dJ06ceP369ZSUlHv37u3YsUNPT496yNdff62jo7Nw4UJCSGJi4vLly7W0tDw9PWfMmNHc3Hzq1KlFixbZ2dnJLzIrFAoXLFhw8eJFb2/vYcOGXbhwISQkRCwWDxkyRNJGJp7ExMRNmzY5ODhQYaenp58+ffrPP//8/vvvu3btSj1k3bp1Ojo6K1euJITEx8fPmjVr+/btkkGx0tLSoKAgLy+vGTNm5OTkpKamlpWVJScnSy4HQJVQwz3Sw0AREaSkBJ/ELURGtljnLSAA4z5MQqbSQvtdcHr27H8eb25qaiooKFi7dm1zc7O3tzeLxbpy5UpFRcXWrVtdXFyoNiNHjpw5c2ZeXp4kU2loaPjqq68kDfbt25ednb18+fL58+ezWKwJEyY4ODiEhobu2bNHUvjC5XITEhKoT3onJ6eZM2eePXvW09Nz4MCBly9fPnv27Mcff2xjYyMfYUZGxqVLl5YvXx4UFMRisXx8fGxtbSNbfuOTjqempiYrK2vYsGHbt2/X0dEhhPj4+ERGRh4+fLi0tFSSqejr60sqiEeOHDl79uzY2FhHR0cWi0U1WL9+va+vLyFk3Lhx2trahw8fLikpaTVCABUgn6wkJ5OSEqxg+5fk5BaDYq6umO/DMGQqLUhPmm9f2sr3g4ODZY5oaGiEhoYOHTqUEOLt7e3t7S19b9euXd977z3pIz179uzbty/1c11dXXp6upGRkZeXl+RjftiwYYMGDcrKygr8+53P2dlZ0iFhaGhoaGhYWVlZV1enq6v7iksQiUSnT582MTEZP348dXIWi+Xp6fm///2vrXi6du26f/9+6XtZLFbPnj1lzjxr1izJRCdTU1NPT88DBw48fPjwgw8+IIQYGxtL9hpksViOjo779u2jOmxeES1AuyafrGC5fQrWeVNCyFRUnPQsZU1NzQEDBgwdOlRmfrJQKLx3715JSUleXt7FixdLS0vt7e0l9xoZGUlyl2fPnvH5fF1d3StXrty8eVPSprm5+dGjR5ISXU3Nl6+rjh07dunSRVIW8woNDQ3V1dVGRkbSwy46OjoGBgbSzaTjoTQ1NZWXl//+++9FRUXZ2dnXrl3r0KFFAZaxsbHMGWpqasrKyqhMpUOHDtIBa2lpvTpOANVArWAm3ZGMZEWmPIUQkpSEdd6Yx0CmwufzY2Jijh8/XldX161bt8mTJ3/22WedO3eWafPNN9+cOXPmxYsXxsbGwcHB06ZNw0fIG5CZpSyjpqZm9erVJ06cEIvFGhoaH3zwwcCBA6urq6XbSH/qi8VikUhUXFwcFhYmcyo9Pb3Hjx+/2+BbJRPP2bNnw8PDqZj19fVtbGxsbW2ls6hWsVgsDQ0NxQYKoPTk11lR82RFZhvCiAiUpygFujOV3377LTAw8NGjR/379+/Xr9+tW7fi4+PT09OlFyKj2lRXV9vb2xsbG2dnZ0dERNy+fTsyMlLRyUr77eV7g6xfLBbHxMScOXNm7dq1Pj4+bDabEFJZWXn16tW2HqKrq2tmZmZkZLR7926qvYyKiorXjuNv2traBgYGt27dEggEkpO/ePHiyZMnXbp0afUhd+/e/fLLL3v37r1hw4YPPviASj7i4uJkMhWZqO7du9elS5cePXq8cagAKqPVZIXDIUlJavchHRkpOy0Z5SlKgtZMRSQS7dq168mTJ1u2bKFqEcRicUJCQlRUlGQhssbGxtjY2KdPn3733Xeenp6EEGqySVpamqen57BhwxQaoVotglRXV3f79m1DQ0M3NzcqMxCLxTwer7y8/MmTJ8+fP5d/iK6u7qBBg+Li4i5cuED9dgghfD4/ICCgW7dusbGx//ikWlpaYrG4ublZ/i5NTc0xY8b88ssvR48epSpqCSE5OTn3798fPHhwq2f7448/qqqqZs2axfl7e/uamprMzMyGhoanT59Kmh09etTb25saVCotLT1//ryNjQ2Hw6HmTgOoOVdXUlxM/v4bIuTvQZCMDDVKVuTTFLXtWFJCtGYqNTU15eXldnZ2Li4ukpJJDw+PvXv35ubmCoVCNptdVFTE4/GcnJxc//4T0dPTW7x4cWBg4JEjR5ydnSWFnPCW2Gy2g4MDj8dbunTpxIkTCSHHjx+/fPmyWCx+9uwZtaSKvLlz5/7666+LFi3y9vZ2dXV9+PDhoUOHKioqli5dKplr8wpmZmZCofD777+vrq52cnKiJuxIuLm5DR06dNOmTYWFhdQs5fT0dPnJzBJWVlYmJiYJCQm1tbW2trYFBQWHDx+uqalpbGxsaGiQNMvNzZ06ders2bOFQmFsbCyLxVqyZImOjk6rC7oAqCFzcyIWEw6nxdiHmxtJSlKL72/Jya0s8obyFOVBa6ZiaGh46NAhmYMVFRU1NTUDBw6kPpB+//33x48fDxkyRPozjMPhmJqa3rp1q6amRqa+Et7Gp59+Sgj573//u3LlSl1dXRcXlxMnTsTFxfF4vJqamlYzDz09ve3bt8fGxv7888+HDx/u2LGjra3tpk2bpItwX8HR0XHChAk///zzpUuXDhw4QNW0SrDZ7JiYmK1bt6akpPz0009WVlbffvvt7t272zpbr169YmNjIyMjk5KSmpubP/jgg9DQUC6XO2/evIKCAkmBzoIFC+rq6tasWUMIcXZ2/uKLL/r06fPv/5UA1ERGBgkMbDEFMjCQPHig4oMgMpN9CFZPUUJi5rx48SIzM3PEiBH9+/e/cOECdTA2NpbD4Zw5c0a6pUAgmDZt2kcfffTgwYNWT7V169atW7e+1rO/wUOAfhUVFcOHD1+2bNmbPfzMmTMcDic2NvbdRsXgi6empqampoaRp2YWLpw2rq5iQlr85+pK5/P/hZ4LLy4Wm5u3uNiICEU/5z9Q25f6K95XGVtNPy4uzsrKiqqc3bNnj7OzM3X8wYMH8o11dXV79uwpFAqliw9A9SQkJHh4eNy9e1dy5PLly+Xl5b1792YwKgC1kpHRYiiE/F1j236Xm2oLVY4jsxatancgtVOMraciEon8/Pz++OOPvLy8uXPnLl++fNasWSwWq9XyCBaLJbNChrzU1NTU1FSZg5s3b25riscrZpQAU4YOHRofHz9v3rw5c+Z07979ypUrP/74I4fDkVmeThkIhcKHDx/S/7xPnz5lsVgCgYD+p2YWLpzOJ50zh+jqai9fbig5Qn2ob9nyZNIkmiJR9IWXlmr6+RmWlr78EJw0Sbh2bQ0Tf9YtqMNLnSptlDlYWlq6ePHiVtszlqlQm8IQQvLz84OCgr799tuBAwfa2Ni0Og9Z3MZsEWmOjo7yFym/XKkE0hQl1L9//507d0ZHR2/YsOHFixf6+vpTpkxZsmSJzHI7ykBbW9vIyIj+59XR0RGLxf+meFnF4MJpft4lS8iECSJLyxafEaGhXa5eZdOzmoNCL7ykhEyfrlla+vKIuTk5eFCbEAb+qGWow0vdyMhIZvFxQoh8X4OEojKV9PR0mXXc4+PjW12CzM7OburUqTt37szNzbWxsTEzM5NvU1dXV15ezmaz9fX123pGU1NTU1PTt48cmGVvby9fdv3G3N3di4qK3tXZpGlqakqvbEsb6kkZeWpm4cLpf+revUlxsWyN7f79mtnZJCND4VNjFHfhJSVk1KgWgz7UnGQleXWpyUv9tT6vGatTkdavXz9CCDXuQ2Uq9+7dk25ALf+lr6/f6mpjAACgCNRHuEzZSkkJ4XBIy51D2w0qePk0BXOSlZmiMhXqu6w0d3f3vLy84cOHh4SEiEQiSUuxWHz58mXy90hN7969u3fvzuPx6uvrJW3u379fUlLSr18/1e4QAwBQQmvWtLIMWkSEbDmq8qNKg6WZm5PiYqQpyo7WPhVzc3M2m33mzJkzZ85IDp49ezYtLY3L5VILcpiamtrZ2fF4vPT0dLFYTAgRCAQxMTHNzc3e3t5Y9g0AgH7UOrYyq4xQH/ztpXMlMlJ290EqTQHlR2umYmhoGBYW1qlTp0WLFk2cOHHVqlU+Pj6ffvopi8VatWoVte+Pjo7O559/rqent3Tp0hkzZoSFhY0aNSo7O9vX19fJyYnOaFVAfX39vn37xo4da2lpyeVyBw4cuGjRojt37kgapKenc7ncuLi4ts4QFhbm4uJSWVlJCBGLxfv37x8wYACXy/3kk08kOye/sbi4uH+zmyANhELh9OnTJVcKAPJaHQki7aFzhVrbTSbygACkKe0G3XUqI0aMOHz48JgxY+7du3fw4MGioiJfX9+ff/55xIgRkjZ2dnY//PCDi4vLr7/+mpaWpqmpGRERQcP2hCpGIBB8/vnnERERtbW1Pj4+/v7+5ubmJ0+e9Pb2Pnny5BucsKCgYNOmTRwOZ/PmzYsXL+7QocOhQ4fk67cBQIVRI0EywyXK3LlCza9OTm5xMCKiHe9Hq4YYqC7mcrnbt29/dRsOh/OKNdTh38jMzDx//vzSpUs/++wzapNhQsjvv/8eGBi4bdu2IUOGGBoavvoMhJDo6GjJzxUVFQKBYP78+dTehDdv3ly/fv1nn32moPgBQDlRI0EyW/oRQiIiSHKyEi2eVlJC9u6VDdLcXIkihH9JKeb+gCJcvHiRzWa7uLhI0hRCSN++fSdPnlxWVsbn89/stOjZAgDSRpltSQmJiJCdXMOIVkd8qK0Hkaa0O8hUVJaZmVlDQ0OJ3BtGWFjYjRs37OzsJEcaGhoSEhLs7e25XK6zs/ORI0eampokjV1cXEpKSqZPn04tkBMcHGxra5uYmOjj4yMQCDZu3CipNWlsbNy3b5+zszOXy7W2tg4JCZHOh8Ri8cWLF8eOHWthYWFjY/P111+/utJFKBRGRUVRZTEeHh6//PKLv7//9OnThUIhVVaybNmyxMREa2trGxubI0eOEELu3LkTFBQ0cOBALpdraWk5duzYkydPUnXZlZWVLi4uy5YtO3r0qJOTE5fLdXJy2rdvn8yayIWFhf7+/paWlvLxA4AMqnNFvnKFmgnM4ciOudCDylHkl/93dSUZGdh6sF1S8bVlXtub/WG97rbotDzLiBEjkpKSli5dmpKSMmHChI8++qhHjx6tTp6KjY3t2bPnwoULtbS09uzZExoaymKxxo8fL2mgpaW1aNEiW1vbXbt2ffrppwMHDjQzM/viiy++++47Dw8PDw8PU1PTxsbGNWvWHDx40MbGJiQkpKqqKjk5OSAgIDk5maqVPnXqVGhoaI8ePVavXk0ISUxMLC8vpzbQlicUChcsWHDx4kVvb+9hw4ZduHAhJCRELBYPGTJE0iY9Pf3GjRurV6+uqKiwsbEpKCgIDAx87733goKCzMzMCgoKUlJSQkNDu3btKqnFTk9Pz8rKGj9+vK2tbWpqakRExJ07dyL+fqMtLS0NCgry8vKaMWNGTk5OampqWVlZcnKynp7ea/3LA6gPc3OyZg2ZPVt2gTjyd8YQGUnfaEurwz0EIz7tHzKVlmQ2//6XXjdTeYNnef3qrz59+hw8ePCLL77IycnJzs4mhOjq6rq5uQUGBtrZ2UmnLB9++GFiYiK1Vs3gwYNnzpxJfZxLGmhpaTk5OQmFQqoBtdbwixcvYmNj+/TpM3r0aEJIVlZWamrqpEmT1q9fT40QOTs7BwUFbdy48dtvv62vr9+9e3evXr0kiYu7u3tAQEBbc20yMjIuXbq0fPnyoKAgFovl4+Nja2sb2bJgr6Gh4auvvnJxcaFubt26tWPHjvHx8VZWVoQQLy8vJyen4ODg/Px8Saby/Pnzb775hqqz8fLyWrVq1ZEjRyZOnEg9hBCyfv16X19fQsi4ceO0tbUPHz5cUlJiY2Pzuv/4AGqFmhaUmUkCA2XHfajxIKp+ZfZsRa1c0laOQrCwm0rA6A/t6Om2IYQQwuFwUlJSeDxedHT02LFjCSHHjh2bPHnyf/7zH+lRj5EjR0qW1DMxMbGwsCgrK6Pykn/v1KlTGhoafn5+kkIWW1tbV1fXK1eulJWVFRUV3b1718fHh0pTqCfy8fFp9VQikej06dMmJibjx4+nMioWi+Xp6WlpaSndrGfPnn379pXcXLJkSU5OjiTnIIQYGBjI9Nk4OTm5/t35q6Wl5efnJxKJ8vPzqSPGxsaSnIbFYjk6OgoEgoqKitf6dwBQW9RgUFJSK2mBpH6FmiL0rqpYSkpIcjJxcyMcTutdKRERWNhNFaBP5a3R0KHydgwNDX19fX19fcVi8e3bt8PDww8cOODo6CjpNZHZYOIft62WV1dXx+fzdXV179+/L91N0tTUJBAIampqqqqqhEKhtbW19KNkbko0NDRUV1cbGRlJD7vo6OgYGBhINzMyMnrvvfdkHltbW/vbb789ePDg8uXLPB5PZj/S7t276+joSG526dKFzWb//vvv1M0OHTpI/1OgdhjgDQQEkICA1vtXyN8pS0TEXyMyhLz2oAx1zsxMkpXV5vc+DPeoGGQqLb1BtdXrjsvQUtBF1ZZ+9NFHGzZskBxksVh9+/Zdt26d/PjOWxKLxSKR6PHjx6tWrZK/t6qq6l09kTSZjKq0tHTZsmV5eXmEkI4dO1pYWAwaNOjcuXP/eB5kJADvHNW/UlJCIiNbzyeolIWQv7IWc/O/3hrNzP7qAuneXVMkEj158jLdefCAZGbKVsPIo3IU9KOoEmQqLcnPumuPT0FI9+7ddXV1r127VlVVJbNuira2dqdOnd7txzObzTYzM3v48OGhQ4eMjY3lG9y8eVNPTy8/P196P22ZfSilIzQwMLh165ZAIJDsSUntUtmlS5dWH1JfX7927dqioqL4+Phhw4Z16tSJetILFy5IN3vy5Mnz58+pewkhFRUVT58+7d279+tfMQD8M8ms4L17SXJym4M+JSWkpEQ+BXm9/WipfhQXF8zuUUGoU1FNBgYG3t7ed+7c2bBhQ21treR4fX19YmLi06dPhw8f/pZPoaGhoampKdls8qOPPqqoqDh27Bg1K5gQIhAIPvnkk5EjRxYXF5ubm/fu3fvkyZOlpaXUvTU1NadPn271zJqammPGjOHz+UePHpWcLScn5/79+20FIxAICgsLLSwsnJycqESkqakpKytLptAkLy/vt99+o35ubGz8+eefO3fu7Ozs/Fb/EADwStT8oOLi1qc0v/3JAwJIRgYpLiZr1iBNUU3oU1FZM2bMKCgo+Omnn06cOGFvb9+rV6/Hjx9fvHjx2bNn06ZNk+7beDPdu3dns9knTpwwNTV1dHT08PC4dOlSVFRUTk7OxIkTa2trDx48WFhYuGLFCnNzcxaL9Z///CcoKGjq1KnUuiyvnqXs5uY2dOjQTZs2FRYWUrOU09PT22pMCDEwMLCzszt27NgXX3wxevTo2tra1NTU27dvs1gs6VIVgUAQEBAwZ84cMzOzvXv33rhxY8WKFX369Hn7PYwA4B9RKcuaNX9N1fk3QzmvOJWrK5k9G6mJWkCmorL09PS2bdvm5eWVkJCQl5eXk5PTsWNHW1vbTz/9VGbh2jdjaGhITUJeunTp5s2bJ0yY8J///MfKyio5OXnZsmUdOnSwtLSkFlyh5u/Y2dn997//Xb169bp16zQ0NEaNGhUcHLxx48ZWT85ms2NiYrZu3ZqSkvLTTz9ZWVl9++23r9hggdocis1mHzly5NSpU/r6+j4+Plu3bv3yyy+Li4slyYqDg8OECRO2bt1aVVVlYWEhHR4A0EaSshDy17jPhAkkNPSv4SFqMEjSUvL/AQOIgQHGd9QRS9K73q5t27aNELJ48WKFPgQYVFlZOWXKFHt7e+mtiF734SYmJvHx8ZLalzfG4IvnyZMnhJC26nVUGC6c6UDohgtnOhC6veJ9FXUqoIwSEhI8PDzu3r0rOXL58uXy8nJUvwIAqBuM/oAyGjp0aHx8/Lx58+bMmdO9e/crV678+OOPHA7H29ub6dAAAIBWyFRAGfXv33/nzp3R0dEbNmx48eKFvr7+lClTlixZ0rlzZ6ZDAwAAWiFTASVlb29/6NChd3W2999/Pysr612dDQAAaIM6FQAAAFBeat2nwuPxmA4B2iUejyfZyxAAABRKfTMVR0dHpkN4BxoaGgghr1gSTVUxe+FOTk6q8foBAFB+6pupODk5qcDXYrWdea+2Fw4AoG5QpwIAAADKC5kKAAAAKC9kKgAAAKC8kKkAAACA8kKmAgAAAMoLmQoAAAAoL2QqAAAAoLwYyFT4fH54eLiNjQ2Xy7W3t4+KiqqtrZVuUF1dPXbsWK6csLAw+qNVcuXl5UyHwAxcuLrBhasbXDhI0J2p/Pbbb76+vikpKVwu19/f39jYOD4+ftKkSXw+X9KmvLy8oqJCV1fXtKWuXbvSHK3yO3369N69e5mOggG4cHWDC1c3uHCQoHWNWpFItGvXridPnmzZsmX8+PEsFkssFickJERFRaWkpCxZsoRqVlFR8eTJk1WrVs2dO5fO8AAAAEDZ0NqnUlNTU15ebmdn5+LiwmKxCCEsFsvDw6Nnz565ublCoZBqVlhYSAjhcrl0xgYAAABKiNY+FUNDw0OHDskcrKioqKmpGThwILXbnFgsvnPnTrdu3UxNTemMDQAAAJQQk3N/Ghsbs7KywsPDNTQ0/P39NTU1CSF1dXVlZWV6enppaWnOzs5cLtfGxiY8PFy6kAUAAADUBGOZSlxcnJWVVWBgYHV19Z49e5ydnanj1dXVDx8+LC4u3r9/f79+/fz8/N5///0ffvjB19f3+vXrTEULAAAAjKB19EeaSCTy8/P7448/8vLy5s6du3z58lmzZrFYrKdPn2poaHz88cffffcdNdmnqakpPj4+Ojo6KioqPj6ezWa3ekIej0fvFSgF9bxqggtXP7hwdYMLVzc8Hs/JyanVu1hisZjmaGTk5+cHBQW9ePFi//79NjY2rbYRCAQBAQF37979/vvvbW1t5RvweLzLly8rOFIAAABQFEdHx1aTFUX1qaSnpwcHB0sfiY+Pd3d3l29pZ2c3derUnTt35ubmtpWp6OnpcTica9euVVVVtdrAycmprVwMAAAA2i+lWE2/X79+hJDGxkbqplAofP78uXwzFouloaFBa2QAAADAKEVlKu7u7kUtubu75+XlDR8+PCQkRCQSSVqKxWJq4KZnz56EkOjo6AEDBiQlJUmfraqqqqCgAFOXAQAA1A2tfSrm5uZsNvvMmTNnzpyRHDx79mxaWhq1BxAhxM3Njc1mp6amFhcXUw3q6+s3b958586d0aNHczgcOgMGAAAAZtFdUXvu3LnQ0NBnz57179+/b9++t27dKigoYLPZW7ZsGTFiBCFEsr6+lpbW8OHDO3funJ2dXVlZ6eDgEBMTY2hoSGe0AAAAwCwG5v4UFRVt3rw5Kyurrq5OV1fXw8NjwYIF5ubmkgZisfj8+fPbt2/Pz89vamoyNjaePXv2tGnT2pqfDAAAAKqK+VnKAAAAAG1Rirk/AAAAAK1CpgIAAADKC5kKAAAAKC/VyVRqa2ujoqLs7e25XK61tfXUqVNzc3PVqgpHKBTOnj07LCyM6UAU686dO/7+/paWlhYWFqNHjz558qRa/ZYJIenp6Y6Ojjdv3mQ6EDqIxeLc3NwpU6ZYWlpyudyPPvooKiqqtraW6bgUrqmp6fjx46NHj7awsLC0tJwyZYq6vaERQgQCgb+/v4uLS2VlJdOxKNzdu3cdHBy4cuLi4pgOTeH4fH54eLiNjQ21Xon837iKZCp8Pn/SpEm7du3q3Lmzn5/foEGDfv31108++eTUqVNMh0aTpqam77//Pjs7m+lAFCs9PX3SpEn5+flubm5jx44tLy9fuHBhQkKC+ryDFxcXR0VFNTQ0MB0IHag1C6ZNm3bz5k03NzdfX9/m5uZdu3YtXLhQIBAwHZ0CiUSir7/+etGiReXl5WPHjvXw8CgsLJw2bZpavdTFYnF8fHxubi7TgdCktLT08ePH+vr6pi3p6ekxHZpiFRQUTJs2LSUlhcvl+vn5de7cuZW/cXH719zcHBkZyeVyd+7cKRKJqINXrlwZMmSIs7PzH3/8wWx4NHj27Nm6deu4XC6Hw1m2bBnT4ShKdXX1hAkThgwZcu3aNepIaWmpu7u7g4NDYWEhs7HRIz8/f9iwYRwOZ8CAATdu3GA6HIUrLCx0cHCgFrymjjx79iw8PJzD4WzZsoXZ2BTqypUrNjY2U6dOra6upo5QL3U1eUOjnD9/3srKisPhDB8+vKKigulwFG737t1cLvfcuXNMB0KrZ8+eBQUFWVlZHTlypLm5WSwWv3jxYuXKlRwOZ//+/ZJmqtCn8ujRo6ysLEtLy8mTJ0s2Bho8ePC4fpOVXQAACsJJREFUceP4fH5hYSGz4SnanTt3pk+fnpiY2LdvX21tbabDUaAbN2789ttvXl5ekv20TUxMFi1a9OjRo3PnzjEbm6LV19fHx8fPnDnz+fPn6rNS84ULF6qqqmbNmiW5ZB0dnTlz5nTv3j03N1coFDIbnuLcvn1bW1vb39+/a9eu1BETE5MxY8aowxsapaqqasOGDX379qV2hVMHv//+e5cuXXr06MF0ILS6evVqVlaWv7//uHHjWCwWIURLS2vatGl6enrXr19vamqimqlIptKhQwdLS0vJXzWlW7duTIVEG6FQGBERUVBQEBoaGhkZqaWlxXRECpSXl9fY2Ojo6Ei9oCnW1tbdunW7cuVKq7taqoycnJxvvvnGxMRk//79AwcOZDocmpSXl3fv3r1v377SB3V1dTt16sRUSPSYMWNGbm7uhAkTJEdEIlFJSYm2tra+vj6DgdFDJBJt27atqqpq5cqVKj/2QREKhaWlpT169KD2v1Mf+fn5GhoaXl5e0u/qNjY2169f37hxo6TrQRUylb59+545cyYmJkZTU1NyUCAQZGRk6OnpqXyK2r9//+PHjy9cuLBjx45Mx6JY5eXlenp6MrtU6uvr6+joPH78WLVLN7S1tcPDww8fPmxpacl0LPT58ssvc3NzqR3BJK5evVpWVmZiYqKrq8tUYDSrqqr6+uuvT58+7ebm1r9/f6bDUbgzZ86kpaUFBwd/+OGHTMdCk9raWj6fr6enFxMTQ80LabWwVMWIxeKioqJu3br16NFj3759zs7ObV24ZlunaNfEYvGBAwfy8/PHjh1rbW3NdDgKxGazV61axXQUdKirq2u1/v+9994zMjL6888/VbtPxdnZ2dnZmekomMfn87/77jtdXd3JkydLfwlTVZWVlVOmTHn48CEhxNfXNyIiQkdHh+mgFIvP52/evNnZ2XnmzJmSzn+Vx+fzHz9+zOfzi4qKnJycOnXqlJ2dvWvXrqysrISE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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [a, b, k] = Vshift(p)\r\n  a = x;\r\n  b = x;\r\n  k = x;\r\nend","test_suite":"%%\r\np = [0.25 -1 -2 0 0];\r\na_correct = 2*(1-sqrt(3));\r\nb_correct = 2*(1+sqrt(3));\r\nk_correct = 64/5;\r\n[a, b, k] = Vshift(p);\r\ntolerance = 1e-13;\r\nassert(abs(a - a_correct) \u003c tolerance)\r\nassert(abs(b - b_correct) \u003c tolerance)\r\nassert(abs(k - k_correct) \u003c tolerance)\r\n\r\n%%\r\np = [0.25 -2 1.5 10 0];\r\na_correct = 2-3*sqrt(2);\r\nb_correct = 2+3*sqrt(2);\r\nk_correct = -3.2;\r\n[a, b, k] = Vshift(p);\r\ntolerance = 1e-13;\r\nassert(abs(a - a_correct) \u003c tolerance)\r\nassert(abs(b - b_correct) \u003c tolerance)\r\nassert(abs(k - k_correct) \u003c tolerance)\r\n\r\n%%\r\nfiletext = fileread('Vshift.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\np = [1 0 0 0 -1];\r\noutput_correct = ['', '', ''];\r\nassert(isequal(Vshift(p), output_correct))\r\n\r\n%%\r\np = [0.5 3 7.5 11 11 8 4];\r\noutput_correct = ['', '', ''];\r\nassert(isequal(Vshift(p), output_correct))\r\n\r\n%%\r\np = [1 -8.5 14 34 -72 0 -17.5];\r\na_correct = -2.094230059318471;\r\nb_correct = 4.727773843365965;\r\nk_correct = 29.244170120692807;\r\n[a, b, k] = Vshift(p);\r\ntolerance = 1e-13;\r\nassert(abs(a - a_correct) \u003c tolerance)\r\nassert(abs(b - b_correct) \u003c tolerance)\r\nassert(abs(k - k_correct) \u003c tolerance)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2026-01-09T14:11:42.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-01-03T12:06:01.000Z","updated_at":"2026-03-25T12:52:10.000Z","published_at":"2026-01-09T14:11:42.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e be an even-degree polynomial with positive leading coefficient. Consider its vertical translation by shifting its graph by its average value over a specified interval \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[a, b], \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ewith \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u0026lt;b\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe interval \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[a, b] \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eis defined such that the endpoints \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stand for the least and the greatest \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-values of the equation \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep(x) = y_peak\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, the lowest and the largest real solutions, respectively. Here, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey_peak\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the highest local maximum of the polynomial \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(see non-scale figures below). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, return \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethe endpoints \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if they exist. Otherwise, return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea = ''\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb = '' \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(see Hint 1);\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethe shifting constant, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, which stands for the above vertical translation (see Hint 2). Return k = '' if the interval is empty.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint 1. An \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-degree polynomial has exactly \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e roots (counting multiplicity) in the complex number system. An odd-degree polynomial always has at least one real root. Therefore, a real polynomial of even degree always has at least one vertex, but might not have local maxima.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint 2. To calculate the mean of a continuous function, use the integral definition.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[a, b, k]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"259\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"370\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"Vertical shift\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"259\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" 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\",\"relationship\":null},{\"partUri\":\"/media/image2.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58259,"title":"Easy Sequences 115: Integral involving square root, floor, and round functions","description":"Given a postive real number , we are asked to evaluate the following integral:\r\n                            \r\n                            where:     the symbol \"\" is the floor function,\r\n                                            and \"\" is the round (to the nearest integer) function.\r\nWe may rewrite the above function in Matlab as:\r\n\u003e\u003e  S = @(n) round(integral(@(x) sqrt(floor(x))-floor(sqrt(x)),0,n));\r\nTherefore, for , we have:\r\n\u003e\u003e  s = S(10*pi)\r\ns =\r\n        12\r\nBe careful though, in using the Matlab integral function, as it is only an approximation. For example if :\r\n\u003e\u003e  s = S(100000)\r\n\r\nWarning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is\r\n8.0e+01. The integral may not exist, or it may be difficult to approximate numerically to the\r\nrequested accuracy. \r\n\u003e In integralCalc/iterateScalarValued (line 372)\r\nIn integralCalc/vadapt (line 132)\r\nIn integralCalc (line 75)\r\nIn integral (line 87)\r\nIn @(n)round(integral(@(x)sqrt(floor(x))-floor(sqrt(x)),0,n)) \r\n\r\ns =\r\n       49841\r\nThe correct answer is . The integral function is off by only 2 units here, but the discrepancy could be even greater for other values of . integral function can also be quite slow. The challenge is to find an efficient and more accurate algorithm to evaluate the integral.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 673px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 445.71875px 336.5px; transform-origin: 445.71875px 336.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven a postive real number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, we are asked to evaluate the following integral:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 48px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 24px; text-align: left; transform-origin: 384px 24px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-18px\"\u003e\u003cimg 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\" width=\"247.5\" height=\"48\" style=\"width: 247.5px; height: 48px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                            where:     the symbol \"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"23.5\" height=\"19\" style=\"width: 23.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\" is the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/help/matlab/ref/floor.html#\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003efloor\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e function,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                                            and \"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"23.5\" height=\"19\" style=\"width: 23.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\" is the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/help/matlab/ref/round.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eround \u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e(to the nearest integer) function.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWe may rewrite the above function in Matlab as:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u0026gt;\u0026gt;  S = @(n) round(integral(@(x) sqrt(floor(x))-floor(sqrt(x)),0,n));\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTherefore, for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"53\" height=\"18\" style=\"width: 53px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, we have:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 60px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 442.71875px 30px; transform-origin: 442.71875px 30px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u0026gt;\u0026gt;  s = S(10*pi)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003es =\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e        12\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eBe careful though, in using the Matlab \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/help/matlab/ref/integral.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eintegral \u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003efunction, as it is only an approximation. For example if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"74\" height=\"18\" style=\"width: 74px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 260px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 442.71875px 130px; transform-origin: 442.71875px 130px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u0026gt;\u0026gt;  s = S(100000)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eWarning: Reached the \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003elimit on the maximum number of intervals in use. Approximate bound on error is\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e8.0e+01. The integral \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003emay not exist\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e, or \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eit may be difficult to approximate numerically to the\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003erequested \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eaccuracy. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u0026gt; In integralCalc/iterateScalarValued (line 372)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eIn \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eintegralCalc/vadapt (line 132)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eIn \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eintegralCalc (line 75)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eIn \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eintegral (line 87)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eIn \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003e@(n)round(integral(@(x)sqrt(floor(x))-floor(sqrt(x)),0,n)) \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003es =\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e       49841\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe correct answer is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"65\" height=\"18\" style=\"width: 65px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. The \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eintegral\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e function is off by only 2 units here, but the discrepancy could be even greater for other values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eintegral\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e function can also be quite slow. The challenge is to find an efficient and more accurate algorithm to evaluate the integral.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = S(n)\r\n    % NOTE: the following expression is inaccurate for some values of n\r\n    s = round(integral(@(x) sqrt(floor(x))-floor(sqrt(x)),0,n)); \r\nend","test_suite":"%%\r\nn = 1:20;\r\ns_correct = [0 0 0 1 1 1 2 2 3 3 3 4 4 5 6 6 6 7 7 7];\r\nassert(isequal(arrayfun(@S,n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = (1:20).*pi;\r\ns_correct = [1 2 3 4 6 7 8 11 11 12 15 16 17 18 20 22 23 24 26 28];\r\nassert(isequal(arrayfun(@S,n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = 100*exp(1);\r\ns_correct = 126;\r\nassert(isequal(S(n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = 1234.5678;\r\ns_correct = 601;\r\nassert(isequal(S(n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = 12345.6789;\r\ns_correct = 6125;\r\nassert(isequal(S(n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = 100000;\r\ns_correct = 49839;\r\nassert(isequal(S(n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = 6e6;\r\ns_correct = 2998571;\r\nassert(isequal(S(n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = 4e8*pi;\r\ns_correct = 628304194;\r\nassert(isequal(S(n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = 10.^(1:10);\r\ns_correct = 5555500618;\r\nassert(isequal(sum(arrayfun(@S,n)),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = (1:1e5).*exp(2);\r\ns = arrayfun(@S,n);\r\nss = round([sum(s) nnz(s) mean(s) median(s) mode(s) std(s) sum(num2str(s))]);\r\nss_correct = [18444149135 100000 184441 184439 303161 106553 37072130];\r\nassert(isequal(ss,ss_correct))\r\nassert(isempty(lastwarn))","published":true,"deleted":false,"likes_count":0,"comments_count":8,"created_by":255988,"edited_by":255988,"edited_at":"2023-05-18T18:10:19.000Z","deleted_by":null,"deleted_at":null,"solvers_count":1,"test_suite_updated_at":"2023-05-18T18:10:19.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-05-04T18:21:04.000Z","updated_at":"2023-05-18T18:10:26.000Z","published_at":"2023-05-05T19:51:12.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven a postive real number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, we are asked to evaluate the following integral:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es=S(n)=\\\\Bigg\\\\lfloor\\\\ \\\\int_0^n\\\\sqrt{\\\\lfloor{x}\\\\rfloor} - \\\\Big\\\\lfloor{\\\\sqrt{x} \\\\Big\\\\rfloor\\\\ \\\\mathrm{d}x\\\\  \\\\Bigg\\\\rceil \\\\cdot\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                            where:     the symbol \\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\lfloor\\\\ \\\\rfloor\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e\\\" is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/matlab/ref/floor.html#\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efloor\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e function,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                            and \\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\lfloor\\\\ \\\\rceil\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e\\\" is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/matlab/ref/round.html\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eround \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e(to the nearest integer) function.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe may rewrite the above function in Matlab as:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[\u003e\u003e  S = @(n) round(integral(@(x) sqrt(floor(x))-floor(sqrt(x)),0,n));]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTherefore, for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=10\\\\pi\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, we have:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[\u003e\u003e  s = S(10*pi)\\ns =\\n        12]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBe careful though, in using the Matlab \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/matlab/ref/integral.html\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eintegral \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003efunction, as it is only an approximation. For example if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=100000\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[\u003e\u003e  s = S(100000)\\n\\nWarning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is\\n8.0e+01. The integral may not exist, or it may be difficult to approximate numerically to the\\nrequested accuracy. \\n\u003e In integralCalc/iterateScalarValued (line 372)\\nIn integralCalc/vadapt (line 132)\\nIn integralCalc (line 75)\\nIn integral (line 87)\\nIn @(n)round(integral(@(x)sqrt(floor(x))-floor(sqrt(x)),0,n)) \\n\\ns =\\n       49841]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe correct answer is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es=49839\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eintegral\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e function is off by only 2 units here, but the discrepancy could be even greater for other values of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eintegral\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e function can also be quite slow. The challenge is to find an efficient and more accurate algorithm to evaluate the integral.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":55335,"title":"Generate Bernoulli polynomials","description":"The Bernoulli polynomial  is a polynomial of order  with the properties that  and for  \r\n,\r\nwhere the prime denotes differentiation with respect to , and\r\n.\r\nTherefore, , , , etc. Notice that  is the th Bernoulli number.\r\nWrite a function to generate the Bernoulli polynomial of order . Use MATLAB's approach for specifying the coefficients. For example, the function should return [1 -1/2] for  and [1 -1 1/6] for .","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 201px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 100.5px; transform-origin: 407px 100.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 78.5917px 8px; transform-origin: 78.5917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Bernoulli polynomial \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"B_n(x)\" style=\"width: 36.5px; height: 20px;\" width=\"36.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 76.2417px 8px; transform-origin: 76.2417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a polynomial of order \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 74.675px 8px; transform-origin: 74.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with the properties that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAH0AAAAoCAYAAADTw/VhAAAFpElEQVR4Xu2aSaseRRSGkx8gjitBEDU7wYDTxmxcOCTgLkSTrRAHEAQxxCgioqCZdjFK3IhiQnQTUBzAjQqKCgoBF8YQXLhyTH6Avg/UgeJQ/XV1dXWl773dcOjv3q7h1HnP3L1503JtOAls3nAnXg68aQF9AyrBAvoC+uwkcK04eln0gujPCtxt1xo3iN6ssNaaXWLOlg7g74n2iX6qKOFntdaNoicqrrmmluoD/Z6M01yqDApbAvgnoqdFX2XwMHTIMU34W3Rg6MSZj78tB4sc0B/UQs+5w34f3C3g3CH6VfSW6APR+QqCORnWnBKUc9rjKdHHFfi93EtgnM+L7hJd08dMH+g2H6u7P/zxqe4PRAsTJz8Kf6MMu0YC/7DmY4lbgmL1naH0OYI602CfUv5y5mHZr0XY4L2qgf6XFrs6cPGY7j4RAqTHw/NXdR9joVggXuP1nFOPHPOd5kNrMb7vFd9Xis6K3g34VAP9Ji2I+7Zrq374xIrkCI3jwtrvLAQDK39fdJ2oRrbex0br/fr4KX1unrga6CYYGAL8WxKcxaB3jck5EFYH2HH4yJlXOoac5A9RynuVrnk55lUHnaSKOM31hijlCmP37mN+rhDMo1CitXDtxldrRcuVx5Bx1UGP4/kj4gQliC/AwqVbzN+h3yUZsXmUbZo/tEyDh+tFPwdPEfNHwraqrDSFzU1qh4DRamxV0MkOf4w497EWgR4VUbZxpZQi9+AWIlI5Q2oNeCOZuU90cxgQJ5E8/zA8I9bBY6qcHLpvzAt7XJF7wBXjhiq5X6oq6D5Be1G73Rp23BkESQw/KPq8Q6i5MjHGcy0O6/5XRA5Axg/w8HK3iKwW70M4IjRRxnSVMijOcVGJh4lL2dxz+nFZyVfP4lVBjw9lDRn2J5kz60KwlHBjW6VDQY/lECsnfJ0SHRb5UJSSHd7qS1FJMveK5t1einaY94/uhLYxVzXQLbM1ZrzbjZsyaOtDojFuagzoBhy8opyfiXJ7BTa3dQI5BmQ/txroHtSUe0TTrUVrrjVVX1ui9bvGd7Vpx4COEP4LkhjqLhfQIxWKAcVdplyQT/R85g7YZMe4sHdELwUrPKK7V46xoNv8oc2hMVVDTWsds1Y1S7fkCGZWxTuzMMbF2TPh4VsRlmcdOv73i4hY6+t9U7LSbpz1E9hvSN/e8oGSRG5dZe85rVdA9pYeK4cJ0yuM1cU+RxiTRdtcs5YhvQJTttyqIbbIdZW957ReOXw8jr9jIM1TeAsygHx3zxRoaBZt86xk8x6nz20CHB6o5H3Busrec1qvCDMOAXH7Nc78Uw0dSqRU7GU9Mu/ct14WQuy9eCqu41kOiVIJpPE59s1gn2JN/bxKTI9brymB2Ldr9jrVZ+5xCdUFOoLwz7Ac1lz1ThhPwfWN6ITotMh69b5ef0bPVn0hYxUKXqLGxx9Tg9u1/mjQfXzEIunEXQw78iUNwFivHTftP1wsBd1yia52brwu7PiqwucYXVWHCQ+PdpWo1Vu9KZTCy6Q3IY2TFwSOZXDvu77QgN9EtF5TdXkp6OxrcTIFhHkYeISH1Ns4rP3eFc/tbKZgub3+Ppm0fo6Md3fg9YP+/7Uo+eKrJGPNOVyc/a9y76n9LU7zzVdOGzWHn9QYXCLCye3cle4zu3lTgc5BLS/woFscXfXe3d6Q8QZtilhLCHtUVJKxzw7EoQxNCbpVAL5mtmSrr9eNcpCV7+kIIUPPauNRKBJAwkeLT7JK+Zxs3pSgW1z39ThfqvBuO6fzZl971gKe9faLntyogKNJU4LO+laC2Rs4a+YM6ZgR42tZJLnGFOFiMqucYuGpQYdnyzIv6DcfN7y9CH4KKPPXbAF6PjfLyCYSWEBvIuZ5bbKAPi88mnCzgN5EzPPaZAF9Xng04WYBvYmY57XJAvq88GjCzf/+Yl845ysLmwAAAABJRU5ErkJggg==\" alt=\"B_0(x) = 1\" style=\"width: 62.5px; height: 20px;\" width=\"62.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25.6667px 8px; transform-origin: 25.6667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"n \u003e 0\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"B'_n(x) = n B_{n-1}(x)\" style=\"width: 113.5px; height: 20px;\" width=\"113.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 169.858px 8px; transform-origin: 169.858px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere the prime denotes differentiation with respect to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 27px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 13.5px; text-align: left; transform-origin: 384px 13.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-8px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Integral[B_n(x),{x,0,1}] = 0\" style=\"width: 80px; height: 27px;\" width=\"80\" height=\"27\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 34.225px 8px; transform-origin: 34.225px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTherefore, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"B_1(x) = x-1/2\" style=\"width: 81px; height: 20px;\" width=\"81\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"B_2(x) = x^2 – x + 1/6\" style=\"width: 121.5px; height: 21px;\" width=\"121.5\" height=\"21\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"B_3(x) = x^3 – 3 x^2/2 + x/2\" style=\"width: 149px; height: 21px;\" width=\"149\" height=\"21\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 52.4917px 8px; transform-origin: 52.4917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, etc. Notice that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"B_n(0)\" style=\"width: 36.5px; height: 20px;\" width=\"36.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 20.6083px 8px; transform-origin: 20.6083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.775px 8px; transform-origin: 7.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45831\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eBernoulli number\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 190.092px 8px; transform-origin: 190.092px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to generate the Bernoulli polynomial of order \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 188.658px 8px; transform-origin: 188.658px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Use MATLAB's approach for specifying the coefficients. For example, the function should return [1 -1/2] for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"n = 1\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 55.2167px 8px; transform-origin: 55.2167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and [1 -1 1/6] for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"n = 2\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = BernoulliPolynomial(n)\r\n  y = sum(nchoosek(n,k).*x.^(0:n));\r\nend","test_suite":"%%\r\nn = 0;\r\ny = BernoulliPolynomial(n);\r\ny_correct = 1;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 1;\r\ny = BernoulliPolynomial(n);\r\ny_correct = [1 -1/2];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 2;\r\ny = BernoulliPolynomial(n);\r\ny_correct = [1 -1 1/6];\r\nassert(all(abs(y-y_correct)\u003c1e-11))\r\n\r\n%%\r\nn = 3;\r\ny = BernoulliPolynomial(n);\r\ny_correct = [1 -3/2 1/2 0];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = 4;\r\ny = BernoulliPolynomial(n);\r\ny_correct = [1 -2 1 0 -1/30];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = 5;\r\ny = BernoulliPolynomial(n);\r\ny_correct = [1 -5/2 5/3 0 -1/6 0];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = 8;\r\ny = BernoulliPolynomial(n);\r\ny_correct = [1 -4 14/3 0 -7/3 0 2/3 0 -1/30];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = 11;\r\ny = BernoulliPolynomial(n);\r\ny_correct = [1 -11/2 55/6 0 -11 0 11 0 -11/2 0 5/6 0];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = 14;\r\ny = BernoulliPolynomial(n);\r\ny_correct = [1 -7 91/6 0 -1001/30 0 143/2 0 -1001/10 0 455/6 0 -691/30 0 7/6];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = 21;\r\ny = BernoulliPolynomial(n);\r\ny_correct = [1 -21/2 35 0 -399/2 0 1292 0 -6783 0 293930/11 0 -223193/3 0 135660 0 -1443183/10 0 219335/3 0 -1222277/110 0];\r\nassert(all(abs(y-y_correct)\u003c2e-9))\r\n\r\n%%\r\nn = 30;\r\ny = BernoulliPolynomial(n);\r\ny_correct = [1 -15 145/2 0 -1827/2 0 28275/2 0 -390195/2 0 4552275/2 0 -43785215/2 0 339319575/2 0 -2062720845/2 0 9509268925/2 0 -31795091601/2 0 72484065225/2 0 -102818379585/2 0 78132595905/2 0 -23749461029/2 0 8615841276005/14322];\r\nassert(all(abs(y-y_correct)\u003c1e-3))\r\n\r\n%%\r\nn = 12;\r\ny = BernoulliPolynomial(n);\r\nn2 = round(y(7));\r\ny2 = BernoulliPolynomial(n2);\r\ny2_15_correct = 373065;\r\nassert(isequal(round(y2(15)),y2_15_correct))\r\n\r\n%%\r\nfiletext = fileread('BernoulliPolynomial.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'switch') || contains(filetext,'regexp'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-09-17T15:39:23.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":"2022-09-17T15:39:23.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-08-20T20:19:44.000Z","updated_at":"2026-01-26T13:39:36.000Z","published_at":"2022-08-20T20:21:33.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Bernoulli polynomial \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B_n(x)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB_n(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a polynomial of order \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e with the properties that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B_0(x) = 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB_0(x) = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n \u0026gt; 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en \u0026gt; 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B'_n(x) = n B_{n-1}(x)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB\\\\prime_n(x) = nB_{n-1}(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere the prime denotes differentiation with respect to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Integral[B_n(x),{x,0,1}] = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\int_0^1 B_n(x) = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTherefore, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B_1(x) = x-1/2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB_1(x) = x – ½\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B_2(x) = x^2 – x + 1/6\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB_2(x) = x^2 – x + 1/6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B_3(x) = x^3 – 3 x^2/2 + x/2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB_3(x) = x^3 – 3 x^2/2 + x/2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, etc. Notice that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B_n(0)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB_n(0)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45831\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBernoulli number\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to generate the Bernoulli polynomial of order \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Use MATLAB's approach for specifying the coefficients. For example, the function should return [1 -1/2] for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n = 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and [1 -1 1/6] for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n = 2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59521,"title":"Integrate a power tower","description":"Write a function to compute this integral\r\n\r\nwhere . That is, the integrand is (x to the x) to the (x to the x) to the (x to the x)...","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 104px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 52px; transform-origin: 407px 52px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 122.783px 8px; transform-origin: 122.783px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute this integral\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQ4AAABYCAYAAAAEERn7AAAPaklEQVR4Xu2dW8hu2xjH174n4YqEbBd2dnHhFNEih5ISckz6Qk4lSXabJEkU9oWUU2ilbKd2EimHKNpyuqDsuNi07MSVU9zz/NY3n/09a6w55xhjHt455vv+33pa33rfMccY8z/G+I8xnucZz7jpkj5CQAgIgUoEbqpMr+RCQAgIgUsiDnUCISAEqhEQcVRDpgeEgBAQcagPCAEhUI2AiKMaMj0gBISAiEN9QAgIgWoERBzVkOkBISAERBzqA0JACFQjIOKohkwPCAEhIOI4TB94pRXznK6oq/bvE03+bHLbYYpXKUJgWQREHMvimeb2EPviuyb/Nnmfya9MvmfyfJP3mnxk3eKVuxBYBwERxzq4kiukcXeX/Yvs3z92f//c/n2qyVM6IlmvBspZCKyEgIhjJWAt26+ZvMLkVd3fXtJfuz8evl7RylkIrIuAiGM6vp+1R59lcp/JVZP3mPyjy+7J9u8vTf5g8ozwPVsUtipfN0HvoY8Q2CUCIo5pzcZq4pkmrBogiW+Z/DSQwUft73ebfMwkKkB9m/JW+/4z04rWU0JgewREHPVtwErhqyY++J0MyMnx7CMIViQoRB9g8lgTdCAoS/URArtDQMRR32ToKB5m8lATtiZuJfmv/f3ALjvXb3zO/v9mE1YgfCCb/5iwOvmxiVYd9fjriQYQEHHUNYLrKL5vj72ge5SVw5NMsJq45eRm+/vLJlhP/mbySRNMr5AGn0+byIejDnulbggBEUddY/hKQj4Ydbgp9ZEhIOKoa1BWDK6j8NVFXQ5K3QICKLSn6Jd47uUmKL5ZSUblONtXfHP4TMm7BVyK6yDiKIbqmvkUpWjUZZQ/rZStIIAZ/fMzB7crv9muftDk/d3L/dr+xXeHz1Hrr0Qc5d3ZtylRv1H+tFK2gACWrX8uMKjd3M4k8jIT+kT8QE539XzfAgaL1EHEUQ6jW1NS34zyHJRySwTYZqCkftoClehTksds/YzSC+1LdwpcoNh2shBxlLUFVpJ7u6QsT9MZpiwXpdoSAczmdyzUdt4f8Ay+ZeCl3AR/lNYzEUdZV36LJcOEykeYlWHWUioG+m9M3M9mbt3QcTzSJPrzpHlSJv46R3kmSYOgrAu5k9fYDFOWk1JtgQDE/xIT972ZUwf0JMRT+ZfJm0w4xPgDE3x50pUoVjjisBydlUXEUdaF3Ayrw2lleLWWCmUlMVGmbhvQjzzX5E8m7zRBd4H1hFUofYLPF3qIg5XJFZOjs7CIOPJd3E+6klKOX3m8hlJM9Z3ADP7SbqA6cbOCQEnNh9kfS8mYEpIB/BOTIeJgWwERvN2E7QdniciTIEx4/37F5NUmv+jSsIJAAfq7rg6QCVa39JMrdwir5r8XceSbiKXph7tkUozm8UpTMMCYmTmnM8fC8D973s2f77K/iaj2YBO2BznfjNIB7GZWJojLJl80gUDicYIaBErLrcmzibQijnwzuH6DlH6wLf+UUjgCzMQfN5m7z3enK/RMMaKal8PvQ+bP0gHsZlbyXGJ1WVru7nqLiCPfZO6/4S7G+SeUwhFgtcaqYKpuISIZVwN9sVrZCn3IpE8BCnmVBodmZUNb32oyZ4VE3SEOYrUcXWxZEcf4II/+G+xvl3AemksrLP05qn/ozoheAR1DzWCCdJcYgGDmJnEPVdCHIwMV9+/UuuGWkJKoa2nYhDntRV4vNpm72ppTh1WeFXGMwxr9N1rwGHWPRJR4h+6M7nlZWvaSJlAP/Pw4e+8xkzhlPtskJQiP0pbzqWBV81oTFKRprNjaAbi070ht+aumF3GMw+vnU0g1tyPNbUgfPK/bgDS87j4AS2ZRsMPpaomVEXqmb5q8wwTyQNfEwGT1E08pU78fmfQ5ev3evh/Djme/ZPIJE5S5vrKBhPosJrn2hMQeY9K3TaMtqX8f+VMP3qlvZYcOZgmvZcrHijTZTFxCHFSWgzyvMeFIuX/QcN9pMvekYa4BtvydzkZH5bP1dQatKNroDwyuGIS5r43AjoE+taMzYNGPIJhcfQDT4d3q8bZukMXy0VFgTk3DHlDvN3T5eHoG0O0mPzThlCurKQYsxws8ABNpp5Af7z+EkW+HUgWsr3D7TmDPOWQJSWEZfJTJ400Yx7OUvyXE4SD7sXL//9YzcF9nXfI7OtXfQ4Y1WC1ZD/LyJXRuqT2lXJ99zuxhfBY8liomTjwj+04DswK4aoKuZejDAB4zX+f8M5iUKB+9iptyGfycOr3HZGjLNFZuauHx7QQOftEXg/d7usnUSG25U7hMAgzgN5rE1Uw8PIffSFx1DAXArmlzb1OemTUR1gyGSBxLaZ1rXvrQaaNpbktXcwY2FgGCx0xeWhaAFzvtb7v03+j+TZfUrjQeI4YccXiVxvwzCqp9Q5JcuZCC36o3Jf/cM2w1IIQxUs3lsdbvTj6zx28NcUS2OoWYFA4yjbjl+6652kg7KIOu9H2ZNXHjHjr/kRvAXnbOP6N2EJWUO1VvUVKXpfQQJWXVpnGsZx+dqCEO35dR2Vn7o9q33Si9g0zxW1pUWEazbD/EDObvXLKM9f14nz4BzOgvZx3pjjVhzj+jtvkhjpL61+a79/Rx6z37Xp9S4oj+DAA41Fn2Dm6svx9s47utXM19e3gofdLQtZV97ep9YmgScUtIbntV4p9R2q+O2gRaCsJAuqhqmD1+S4kj+jOk1xrOfJ8mH2+FKH17eAhXd5bYV0zwYRhzskrJ9WcdsaYNWeJ0VeqfUdpJlvQdKS1zL+l8Ulhk/JYSR/RnmL0/2gHSkZ23DE7sW4fSdvJTnpcNY6wCaUR2d+LCehLb0Qcw5lNWCq4MzukCqB8BbfqsPa7UHQueU+qfUdpl6Kd9x9tLnz+WdBDomcmDOvGAyn2TAm1MzBDuQcb1IB3fbCXZ2lzXl0o7ZNRvzFk2R73B1EY6xECOitEtXc3ZLmF6LHV1p8MQMwLHI49Y5h3BnaP+0nUQyAGrCflzbN1vlvO2pp1fbzIW/CZHbOBIfeJ2Zap/Rq6/+CVYpVjl8tvj7+6gB1m7qdeP/0MafOL4BbPndW0EuTCh8PGtjN+RTH4Qx/26kRLiiPEoyHTOsnkvxBHrWbpsX6OjoeibSlzuvOZL07strw+Y0BloU3wEvmPyCJPor+BhBKL/xNC7OcEO7ZnptB7Lwn0SfPtV65+Rw3epU7i5clr9nUnDY5SkUce8PzPp4gTW55UaV9mQC453ZyacOOZzXYSzEuKI8SimduJWwR6qV1SMztZAz3j5OcSRms/xzVjilGp8HSeOMeUxs9qnTFKHphmw3PAofZSVzRTX8CXrsVVecXLv2xE4cYyN32h1IR3bnL7wBdfesYQ4YjyKLc2Sh2qUVDG6pWlvDnHEGYSOsEao/hLioN38ft2p7udjbT927uNQfWbLclyXxFZiSP/o/jk5N4p4xGJUJVFCHC2YJQ/ZMKlrfQlGa9VvDnHEGWSt7dYhrT5rYbz3fL0N2IZwpqfvjA6TP5/cJBhXqaMqidygiEug2W6qO2mhVhSjwIWi8j6TqQo/V3Su5fmaU47upMl3W804OQy1sVtES8ZvdLsYJZkccSztdr0H5WgrilF685yBGduudFtaO4KoH3vhW2ofVPpFEIj6xz5dXMk2xisS0/LdqFoiRxxxEOX2RyVI7IE4WlGMgmfOajGEuZ8i5Sj1moGW2Uqdgl9PSd/eIk30r+qzbMWtR07Jz9hEge7+HKOGkBxxuFIFUGa7qW6BbGWZ6VH63J6wMvvq5L5VrPGd8ZmDGCrcnu6hAeIMwkw1JcZEfAGvW65DVr+0HihGIE7EqU4inu6O4xcySc89MUE9wQTLF/2CcAZ8nB/Ii2jv95+SHiOOUztGD1Ap2DliLW7hGQnRU3CV4Fi8TOqNUozGxV+DSFZODK4p9xmEWao0cO9Ytd2jcMgvYMYr69FCBOKKI5rE/fgA+jGcutyXB38d2h7ywHqIXgS9Bh7DbnqN45486VP0p+tMs2MDI5pht4xHUYjhIslaUoz6C+UGaNznolnnEiEPfEMecbmKggwSir9PBa6E0KbmrefKEIgTHW0PMUDkmN5ZcUZvUEiCaytpe8gD8y3P8CGtm8rjqpvf2bqfhd+vPdBHHM5A+K3HDxkT9zF32rHsldtMFRm8FZ+VXCAfZgjCN9IRMLtCJNEz0C8/9nMK6e9TWsJ1KH3mvyn56ZnpCNCefgOdTxzoI1mB+qTCxE+4Rx+7vsVhIrmBFOy7GPCn7/ciB7Dpr7S/J4sdYA78ak4OrWwLwOnbJkt7oh4YVhU3FYEW9vBT677Gcy0rg92dekzXsQYmaZ7MRmjep/qWHKKOKmNlBEQcFwCnzm5rBAae25wsMa+EJefc/GqfZ4tSEuG8Nl+l3xkCIo6LBova5LU8LZfoHqw8/Aj8EvmV5uGxPNY481JaB6VrBAERx0VDRIvKEs5uazZxLsDOGmVvUeYa76E8F0BAxHEBYjQ/b+34tUDTKgshsB4CIo4LbKNFRbis1+eU8xEgoAFy0YhuUTmVYEVH0H31ClshIOI4Rz564LXi+LVVn1C5QiCLgIjjHKIYh2CrO1SyjaUEQqAVBEQc5y0Rz3MIk1Z6p+rRLAIaJOdNUxLMtdlGVMWEwKEREHGcI+7Be4b0Gxw083tKSM+ZEQ4Wpbe4H7r9VJ4Q2AQBEcd5XIJ7O/T79Bt+OpWrDj3Ev586lL/HJt1WhW6NgIjjesVoHx5+1D4lFVYp3IqmeJtb92KVf3AERBwXitG+8ykxqEkams31IrLCHLzbqsCtERBxXLrkHqN951Pcv6MvApqfbVnrzpKt+4bKFwKDCJw6ccQVRV8wZieHMeKQp6kG2MkhcOrE4Ufph2KqlhDHqcRjPbnBoRceRuDUicMdv4aO0Ys4NHqEQA8Cp04cfkXi0J0xMdhraj0ZIxV1NiFw1AicAnGgx7jdhPsh4iVErvgcu4lMytGj7v56uakInAJxxMhe0XTq5tTcDXV+3D7Fyp+vuWVtajvpOSHQFAKnQBzxwiL39PSVRMkR+jEHMJzAbjWJ95g01cCqjBBYA4FTIA62KlyL6PeA+GVCd9p36R2afRi7y/k99qNfCeBkpNXGGr1SeTaPwCkQB43A4IckLptcNbnLxK+8K2kkzrNw6zuH27jR+9Emd1TmUVKO0giBXSBwKsSxi8ZQJYXAXhAQceylpVRPIdAQAiKOhhpDVRECe0FAxLGXllI9hUBDCIg4GmoMVUUI7AUBEcdeWkr1FAINISDiaKgxVBUhsBcE/g+tfmSG+LdlUAAAAABJRU5ErkJggg==\" width=\"135\" height=\"44\" alt=\"I = integral((x^x)^(x^x)^(x^x)...,{x,a,0})\" style=\"width: 135px; height: 44px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"63\" height=\"18\" style=\"width: 63px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 226.3px 8px; transform-origin: 226.3px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. That is, the integrand is (x to the x) to the (x to the x) to the (x to the x)...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function I = intPowerTower(a)\r\n  I = integral(x^x^x^x^x^x^x^x,0,a);\r\nend","test_suite":"%%\r\na = 0;\r\nI = intPowerTower(a);\r\nassert(abs(I)\u003c1e-6)\r\n\r\n%%\r\na = 1/100;\r\nI = intPowerTower(a);\r\nI_correct = 0.00975627404012066;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 1/20;\r\nI = intPowerTower(a);\r\nI_correct = 0.04621245261821598;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 1/10;\r\nI = intPowerTower(a);\r\nI_correct = 0.0886781687569094;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 1/5;\r\nI = intPowerTower(a);\r\nI_correct = 0.1685639964895788;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 1/4;\r\nI = intPowerTower(a);\r\nI_correct = 0.2071658901263798;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 3/8;\r\nI = intPowerTower(a);\r\nI_correct = 0.30215124860335973;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 1/2;\r\nI = intPowerTower(a);\r\nI_correct = 0.3972053202401857;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 2/3;\r\nI = intPowerTower(a);\r\nI_correct = 0.5277402852630483;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 3/4;\r\nI = intPowerTower(a);\r\nI_correct = 0.5959989560650945;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 5/6;\r\nI = intPowerTower(a);\r\nI_correct = 0.6671963910854818;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = 1;\r\nI = intPowerTower(a);\r\nI_correct = 0.822467033424113;\r\nassert(abs(I-I_correct)\u003c1e-8)\r\n\r\n%%\r\na = (rand+3)/4;\r\nI = intPowerTower(a);\r\nI_correct = polyval([0.3875275 -0.9886411 1.132527 0.1505356 0.1405179],a);\r\nassert(abs(I-I_correct)\u003c5e-6)\r\n\r\n%%\r\nfiletext = fileread('intPowerTower.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp') || contains(filetext,'find') || contains(filetext,'switch'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":46909,"edited_by":46909,"edited_at":"2024-01-03T15:06:22.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-12-31T18:50:11.000Z","updated_at":"2026-01-28T06:58:04.000Z","published_at":"2023-12-31T18:50:21.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute this integral\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"I = integral((x^x)^(x^x)^(x^x)...,{x,a,0})\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eI = \\\\int_0^a {(x^x)^{(x^x)^{(x^x)\\\\ldots}} dx\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e0 \\\\le a \\\\le 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. That is, the integrand is (x to the x) to the (x to the x) to the (x to the x)...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59541,"title":"Compute the polylogarithm for real arguments","description":"The polylogarithm  appears in quantum statistics and quantum electrodynamics, and for special cases of  and , it connects to the logarithm, ratios of polynomials, the zeta function, the Dirichlet eta function, and other functions. \r\nWrite a function to compute the polylogarithm  for real arguments. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 74px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 37px; transform-origin: 407px 37px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 57.575px 8px; transform-origin: 57.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe polylogarithm \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"39\" height=\"20\" alt=\"Li_n(z)\" style=\"width: 39px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 267.225px 8px; transform-origin: 267.225px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e appears in quantum statistics and quantum electrodynamics, and for special cases of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ez\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.325px 8px; transform-origin: 9.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, it connects to the logarithm, ratios of polynomials, the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45988\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003ezeta\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45997\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003efunction\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 146.242px 8px; transform-origin: 146.242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the Dirichlet eta function, and other functions. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 142.233px 8px; transform-origin: 142.233px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the polylogarithm \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAE4AAAAoCAYAAABQB8xaAAAELklEQVRoQ+2aS6gPURzH792TYkVCWFDEwquUhUSJhPJOVh4LyYJiYUldNrLwyEJWHlnYKBYspDxWSrFA2bDyKnu+n5pfnc6dc+bMmfnf6X/N1Lf//c9/zsw5n/M7v8eZOzrSH1kERrNa9Y1GenCZRtCD+4/BrdTY50t3MxksULsVddsPu8UB7Yq0WfqRCY5mY9JcaXfqPYYZHNBuS2sbQjNWZrFJ8Hxw13WXddKiEvIfdO63tCZ1VnQdy+C5NFXaKT2p0TZ26XT9+KXle/K8l9It6VpVP0MWd0YNzzuN79UxY6cdS+BU8R1om6o6lPg7AwRcknUk3pPLsOKn0nLpU6xdbKn+dRqu0t9vanTALjWL4/tJKdeBu4/eqC+PpYVVg8voL03oI/4uurIGDS6z79Fmg7I2e6hNTNRYhg0cS+m1tKcl6w3N0Ff9gG8OuoJhA0fwOizNkJqkH1UrgeVKikNQKz0mClzTJNU6/774Y3HVyBv+bsExuFwHCY7AsEs6Ls2U2oiqBKxXVY67gEYAmRYBSGoVivLm547pmtLUZFDggHZEWibRCY6m4My/XdS9TldYFM//WHEN0EJ5pYELPmtQ4Nw+W1rTFFzlYJyHstQOFnLTKBLnFxIVx4UKsPQ7mL9OVnAk3vclP/dk+f6SUhLnqFuYrODKjImIPE/aK6VE5B6cQB2VTkhbpGgpVRBnSX+Xbkj46nHHMFmcOfyU4OAOlKDyUNpWsnRDbq7Snw4CHA91o1VbwYFB1klHuD53F8XABSuUtsHxwAeSm3G3CY46dY40K2Qq3nkS5pQI6t/OdnWCGwltgysrwNsEZxl9SslF2UQELfVRFeCJvktjE9QmODpKpeBn2yFwliSzcYoVse30WWIrfLVU5pjNzwUz+gIIgNlT47qUCOpzpM9RXxoCRxS66tyNMudcYJY26PwBibLqj7ResvzJzeDZQS6rMenktwLcDn1ektgB4VzZksSqOUL7ZeafuIYE9qyUEklteDb26H6fD45G2yUrkwKsgqcNDsAoi7YWQK0Bv7s+x8ooJoZjf/FJuRSqSWMbmbaDO8XroVusM8ZDxbPKgDIxb6XoEu/6ZY35LCzV3knYjGMpobKIZJY62Lc6KoKfhYUxcJYqELHeJRLLFjAhV0D7mxI7wNEl3jU4G4RbE5qvjO3AWs15WQOMvVjhOlwOvpcUiaqBydgnuS4FA62VunQNDv/m+0V2XznMQoqv4z4Y6DspJbE114GV8pIHP+rXsclvuOhJl+DMV7m7JhZMsEAGxxF7SQS8RxJ7fjkvk2w2sPJnUuVrQWvQJThLMl1fZj6Pc6QTZZbhmx7w+BeG3He2TBb3qAW+S3Bk9bMLQBbdcM53JKIvRXkuDB9u69+7BNf6YCbyhj24TNo9uB5cJoHMZr3F9eAyCWQ26y0uE9w/mWQQOMc8jDwAAAAASUVORK5CYII=\" width=\"39\" height=\"20\" alt=\"Li_n(z)\" style=\"width: 39px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 62.6167px 8px; transform-origin: 62.6167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for real arguments. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = polylogarithm(n,z)\r\n  y = sum(z^k/k^n);\r\nend","test_suite":"%%\r\nn = 2:2:16;\r\nz = 1;\r\ny = arrayfun(@(m) polylogarithm(m,z),n);\r\ny_correct = pi.^n.*[1/6 1/90 1/945 1/9450 1/93555 691/638512875 2/18243225 3617/325641566250];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = 3;\r\nz = 1;\r\ny = polylogarithm(n,z);\r\ny_correct = 1.202056903159594;\r\nassert(abs(y-y_correct)\u003c1e-12)\r\n\r\n%%\r\nn = 0;\r\nz = 1./(10:-1:2);\r\ny = arrayfun(@(s) polylogarithm(n,s),z);\r\ny_correct = 1./(9:-1:1);\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = 1;\r\nz = [-2 -3/2 -1 -1/2 0 1/10 1/7 1/5 1/3 1/2];\r\ny = arrayfun(@(s) polylogarithm(n,s),z);\r\ny_correct = [-1.098612288668110 -0.916290731874155 -0.693147180559945 -0.405465108108164 0 0.105360515657826 0.154150679827258 0.223143551314210 0.405465108108164 0.693147180559945];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = -1;\r\nz = [-2 -3/2 -1 -1/2 1/7 1/5 1/2];\r\ny = arrayfun(@(s) polylogarithm(n,s),z);\r\ny_correct = [-2/9 -6/25 -1/4 -2/9 7/36 5/16 2];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = -2;\r\nz = [-2 -3/2 -1 -1/2 0 1/17 1/13 1/11 1/5];\r\ny = arrayfun(@(s) polylogarithm(n,s),z);\r\ny_correct = [2/27 6/125 0 -2/27 0 153/2048 91/864 33/250 15/32];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = 1:3;\r\nz = 1/2;\r\ny = arrayfun(@(m) polylogarithm(m,z),n);\r\nzeta3 = 1.202056903159594;\r\ny_correct = [log(2) (pi^2-6*log(2)^2)/12 (4*log(2)^3-2*pi^2*log(2)+21*zeta3)/24];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = 2;\r\nz = -1;\r\ny = polylogarithm(n,z);\r\ny_correct = -pi^2/12;\r\nassert(abs(y-y_correct)\u003c1e-12)\r\n\r\n%%\r\nn = -1/pi;\r\nz = exp(-1);\r\ny = polylogarithm(n,z);\r\ny_correct = 0.6541056465726233;\r\nassert(abs(y-y_correct)\u003c1e-12)\r\n\r\n%%\r\nn = 4;\r\nz = 1/2;\r\ny = polylogarithm(n,z);\r\ny_correct = 0.5174790616738994;\r\nassert(abs(y-y_correct)\u003c1e-12)\r\n\r\n%%\r\nn = 1/2;\r\nz = 1/2;\r\ny = polylogarithm(n,z);\r\ny_correct = 0.8061267230428522;\r\nassert(abs(y-y_correct)\u003c1e-12)\r\n\r\n%%\r\nn = -3/2;\r\nz = -1./2.^(1:4);\r\ny = arrayfun(@(s) polylogarithm(n,s),z);\r\ny_correct = [-0.1516441361365191 -0.1313580923579523 -0.0892942267818043 -0.05260782861980105];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = 5*randn(1,randi(10));\r\nz = 0;\r\ny = arrayfun(@(m) polylogarithm(m,z),n);\r\ny_correct = zeros(size(n));\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nfiletext = fileread('polylogarithm.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2024-01-07T03:51:00.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-01-06T17:30:34.000Z","updated_at":"2025-02-27T16:14:20.000Z","published_at":"2024-01-06T17:31:22.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe polylogarithm \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Li_n(z)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e{\\\\rm Li}_n(z)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e appears in quantum statistics and quantum electrodynamics, and for special cases of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" 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