How to set the boundary value of the integral function as a variable

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Xiuyu Yang
Xiuyu Yang el 23 de Jun. de 2021
Comentada: Xiuyu Yang el 23 de Jun. de 2021
Hallo, I have a trouble with integral function. I want to calculate the coincident area of two Geometric shape. one is
rectangle, the other is circle. But the retangle can move with variable t.
So I don't know how to use the function command and integral function correct.
f=@(x)sqrt(3600-x^2)-10
so I write this function to calculate the coincident.area and at this moment the boundary is [-10, 10].
But if I want to let the boundary as variable such as [t-10,t+10] t=[-70:70]
And I want to get all the coincident area when the rectangle through pass the circle.
so how can I make it possible?

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Walter Roberson
Walter Roberson el 23 de Jun. de 2021
Ran in:
format long g
f = @(x)sqrt(3600-x^2)-10
f = function_handle with value:
@(x)sqrt(3600-x^2)-10
t = (-70:70).';
syms x T
F = int(f(x), x, T-10, T+10)
F = 
val = [t, double(subs(F, T, t))]
val =
-70 + 0i -200 + 684.943218648642i -69 + 0i -192.715317242383 + 632.788260102101i -68 + 0i -179.447677765181 + 582.170744380302i -67 + 0i -162.338556138325 + 533.118473240453i -66 + 0i -142.164021394958 + 485.66200081327i -65 + 0i -119.378682275273 + 439.835074992098i -64 + 0i -94.2933676203167 + 395.675182131565i -63 + 0i -67.1393073019813 + 353.224228116603i -62 + 0i -38.0980571980923 + 312.529402746931i -61 + 0i -7.31765272910584 + 273.64429572218i -60 + 0i 25.0777806340218 + 236.63036634635i -59 + 0i 58.9818952700149 + 201.558924679513i -58 + 0i 94.3019958279119 + 168.513877221217i -57 + 0i 130.956145591515 + 137.595662217478i -56 + 0i 168.87106748014 + 108.927129708049i -55 + 0i 207.980578579849 + 82.6628054053041i -54 + 0i 248.224395011907 + 59.0045435848361i -53 + 0i 289.547201179215 + 38.230678550478i -52 + 0i 331.897912335059 + 20.7588853315027i -51 + 0i 375.229081484929 + 7.32119777088167i -50 + 0i 419.496416022359 + 0i -49 + 0i 457.373696383673 + 0i -48 + 0i 490.123535447779 + 0i -47 + 0i 519.850438846141 + 0i -46 + 0i 547.29541379786 + 0i -45 + 0i 572.879711593697 + 0i -44 + 0i 596.882333345185 + 0i -43 + 0i 619.504059488799 + 0i -42 + 0i 640.897242661197 + 0i -41 + 0i 661.181845337652 + 0i -40 + 0i 680.454948113859 + 0i -39 + 0i 698.796791187679 + 0i -38 + 0i 716.274819231228 + 0i -37 + 0i 732.94650282475 + 0i -36 + 0i 748.861372588717 + 0i -35 + 0i 764.062526138083 + 0i -34 + 0i 778.587770223787 + 0i -33 + 0i 792.470503318548 + 0i -32 + 0i 805.740409103958 + 0i -31 + 0i 818.424009335318 + 0i -30 + 0i 830.545110241798 + 0i -29 + 0i 842.125167037671 + 0i -28 + 0i 853.18358455535 + 0i -27 + 0i 863.737967417832 + 0i -26 + 0i 873.804329894155 + 0i -25 + 0i 883.397273208314 + 0i -24 + 0i 892.530136325691 + 0i -23 + 0i 901.215124938123 + 0i -22 + 0i 909.463422384336 + 0i -21 + 0i 917.285285490241 + 0i -20 + 0i 924.690127732511 + 0i -19 + 0i 931.686591675735 + 0i -18 + 0i 938.282612276683 + 0i -17 + 0i 944.485472366114 + 0i -16 + 0i 950.301851391957 + 0i -15 + 0i 955.737868325008 + 0i -14 + 0i 960.799119479948 + 0i -13 + 0i 965.490711883193 + 0i -12 + 0i 969.817292719193 + 0i -11 + 0i 973.783075304097 + 0i -10 + 0i 977.391861966658 + 0i -9 + 0i 980.647064158323 + 0i -8 + 0i 983.55172006547 + 0i -7 + 0i 986.108509955024 + 0i -6 + 0i 988.319769448928 + 0i -5 + 0i 990.18750089195 + 0i -4 + 0i 991.713382950254 + 0i -3 + 0i 992.898778554309 + 0i -2 + 0i 993.744741278364 + 0i -1 + 0i 994.252020229412 + 0i 0 + 0i 994.421063500843 + 0i 1 + 0i 994.252020229412 + 0i 2 + 0i 993.744741278364 + 0i 3 + 0i 992.898778554309 + 0i 4 + 0i 991.713382950254 + 0i 5 + 0i 990.18750089195 + 0i 6 + 0i 988.319769448928 + 0i 7 + 0i 986.108509955024 + 0i 8 + 0i 983.55172006547 + 0i 9 + 0i 980.647064158323 + 0i 10 + 0i 977.391861966658 + 0i 11 + 0i 973.783075304097 + 0i 12 + 0i 969.817292719193 + 0i 13 + 0i 965.490711883193 + 0i 14 + 0i 960.799119479948 + 0i 15 + 0i 955.737868325008 + 0i 16 + 0i 950.301851391957 + 0i 17 + 0i 944.485472366114 + 0i 18 + 0i 938.282612276683 + 0i 19 + 0i 931.686591675735 + 0i 20 + 0i 924.690127732511 + 0i 21 + 0i 917.285285490241 + 0i 22 + 0i 909.463422384336 + 0i 23 + 0i 901.215124938123 + 0i 24 + 0i 892.530136325691 + 0i 25 + 0i 883.397273208314 + 0i 26 + 0i 873.804329894155 + 0i 27 + 0i 863.737967417832 + 0i 28 + 0i 853.18358455535 + 0i 29 + 0i 842.125167037671 + 0i 30 + 0i 830.545110241798 + 0i 31 + 0i 818.424009335318 + 0i 32 + 0i 805.740409103958 + 0i 33 + 0i 792.470503318548 + 0i 34 + 0i 778.587770223787 + 0i 35 + 0i 764.062526138083 + 0i 36 + 0i 748.861372588717 + 0i 37 + 0i 732.94650282475 + 0i 38 + 0i 716.274819231228 + 0i 39 + 0i 698.796791187679 + 0i 40 + 0i 680.454948113859 + 0i 41 + 0i 661.181845337652 + 0i 42 + 0i 640.897242661197 + 0i 43 + 0i 619.504059488799 + 0i 44 + 0i 596.882333345185 + 0i 45 + 0i 572.879711593697 + 0i 46 + 0i 547.29541379786 + 0i 47 + 0i 519.850438846141 + 0i 48 + 0i 490.123535447779 + 0i 49 + 0i 457.373696383673 + 0i 50 + 0i 419.496416022359 + 0i 51 + 0i 375.229081484929 + 7.32119777088167i 52 + 0i 331.897912335059 + 20.7588853315027i 53 + 0i 289.547201179215 + 38.230678550478i 54 + 0i 248.224395011907 + 59.0045435848361i 55 + 0i 207.980578579849 + 82.6628054053041i 56 + 0i 168.87106748014 + 108.927129708049i 57 + 0i 130.956145591515 + 137.595662217478i 58 + 0i 94.3019958279119 + 168.513877221217i 59 + 0i 58.9818952700149 + 201.558924679513i 60 + 0i 25.0777806340218 + 236.63036634635i 61 + 0i -7.31765272910584 + 273.64429572218i 62 + 0i -38.0980571980923 + 312.529402746931i 63 + 0i -67.1393073019813 + 353.224228116603i 64 + 0i -94.2933676203167 + 395.675182131565i 65 + 0i -119.378682275273 + 439.835074992098i 66 + 0i -142.164021394958 + 485.66200081327i 67 + 0i -162.338556138325 + 533.118473240453i 68 + 0i -179.447677765181 + 582.170744380302i 69 + 0i -192.715317242383 + 632.788260102101i 70 + 0i -200 + 684.943218648642i
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Walter Roberson
Walter Roberson el 23 de Jun. de 2021
Ran in:
I transposed for display purposes only.
format long g
f = @(x)sqrt(3600-x^2)-10
f = function_handle with value:
@(x)sqrt(3600-x^2)-10
t = -70:70;
syms x T
F = int(f(x), x, T-10, T+10)
F = 
val = double(subs(F, T, t))
val =
-200 + 684.943218648642i -192.715317242383 + 632.788260102101i -179.447677765181 + 582.170744380302i -162.338556138325 + 533.118473240453i -142.164021394958 + 485.66200081327i -119.378682275273 + 439.835074992098i -94.2933676203167 + 395.675182131565i -67.1393073019813 + 353.224228116603i -38.0980571980923 + 312.529402746931i -7.31765272910584 + 273.64429572218i 25.0777806340218 + 236.63036634635i 58.9818952700149 + 201.558924679513i 94.3019958279119 + 168.513877221217i 130.956145591515 + 137.595662217478i 168.87106748014 + 108.927129708049i 207.980578579849 + 82.6628054053041i 248.224395011907 + 59.0045435848361i 289.547201179215 + 38.230678550478i 331.897912335059 + 20.7588853315027i 375.229081484929 + 7.32119777088167i 419.496416022359 + 0i 457.373696383673 + 0i 490.123535447779 + 0i 519.850438846141 + 0i 547.29541379786 + 0i 572.879711593697 + 0i 596.882333345185 + 0i 619.504059488799 + 0i 640.897242661197 + 0i 661.181845337652 + 0i 680.454948113859 + 0i 698.796791187679 + 0i 716.274819231228 + 0i 732.94650282475 + 0i 748.861372588717 + 0i 764.062526138083 + 0i 778.587770223787 + 0i 792.470503318548 + 0i 805.740409103958 + 0i 818.424009335318 + 0i 830.545110241798 + 0i 842.125167037671 + 0i 853.18358455535 + 0i 863.737967417832 + 0i 873.804329894155 + 0i 883.397273208314 + 0i 892.530136325691 + 0i 901.215124938123 + 0i 909.463422384336 + 0i 917.285285490241 + 0i 924.690127732511 + 0i 931.686591675735 + 0i 938.282612276683 + 0i 944.485472366114 + 0i 950.301851391957 + 0i 955.737868325008 + 0i 960.799119479948 + 0i 965.490711883193 + 0i 969.817292719193 + 0i 973.783075304097 + 0i 977.391861966658 + 0i 980.647064158323 + 0i 983.55172006547 + 0i 986.108509955024 + 0i 988.319769448928 + 0i 990.18750089195 + 0i 991.713382950254 + 0i 992.898778554309 + 0i 993.744741278364 + 0i 994.252020229412 + 0i 994.421063500843 + 0i 994.252020229412 + 0i 993.744741278364 + 0i 992.898778554309 + 0i 991.713382950254 + 0i 990.18750089195 + 0i 988.319769448928 + 0i 986.108509955024 + 0i 983.55172006547 + 0i 980.647064158323 + 0i 977.391861966658 + 0i 973.783075304097 + 0i 969.817292719193 + 0i 965.490711883193 + 0i 960.799119479948 + 0i 955.737868325008 + 0i 950.301851391957 + 0i 944.485472366114 + 0i 938.282612276683 + 0i 931.686591675735 + 0i 924.690127732511 + 0i 917.285285490241 + 0i 909.463422384336 + 0i 901.215124938123 + 0i 892.530136325691 + 0i 883.397273208314 + 0i 873.804329894155 + 0i 863.737967417832 + 0i 853.18358455535 + 0i 842.125167037671 + 0i 830.545110241798 + 0i 818.424009335318 + 0i 805.740409103958 + 0i 792.470503318548 + 0i 778.587770223787 + 0i 764.062526138083 + 0i 748.861372588717 + 0i 732.94650282475 + 0i 716.274819231228 + 0i 698.796791187679 + 0i 680.454948113859 + 0i 661.181845337652 + 0i 640.897242661197 + 0i 619.504059488799 + 0i 596.882333345185 + 0i 572.879711593697 + 0i 547.29541379786 + 0i 519.850438846141 + 0i 490.123535447779 + 0i 457.373696383673 + 0i 419.496416022359 + 0i 375.229081484929 + 7.32119777088167i 331.897912335059 + 20.7588853315027i 289.547201179215 + 38.230678550478i 248.224395011907 + 59.0045435848361i 207.980578579849 + 82.6628054053041i 168.87106748014 + 108.927129708049i 130.956145591515 + 137.595662217478i 94.3019958279119 + 168.513877221217i 58.9818952700149 + 201.558924679513i 25.0777806340218 + 236.63036634635i -7.31765272910584 + 273.64429572218i -38.0980571980923 + 312.529402746931i -67.1393073019813 + 353.224228116603i -94.2933676203167 + 395.675182131565i -119.378682275273 + 439.835074992098i -142.164021394958 + 485.66200081327i -162.338556138325 + 533.118473240453i -179.447677765181 + 582.170744380302i -192.715317242383 + 632.788260102101i -200 + 684.943218648642i
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