Numerical method MATLAB code

Question

Shoaib Salim el 6 de Abr. de 2023

0
Enlazar

Enlace directo a esta pregunta

https://es.mathworks.com/matlabcentral/answers/1942789-numerical-method-matlab-code

Comentada: Oguz Kaan Hancioglu el 7 de Abr. de 2023

I am unable to get plot of following code of numerical methods. Plot command throw error of not same vector length

% Title: Comparison of Trapezoid and Simpson's Composite Methods for T-distribution and Normal Distribution
% Name: TXXXX XXXXXXX
% Class: Scientific Computing
% Define the probability density functions for T-distribution and normal distribution
f_t = @(x, v) gamma((v+1)/2) / (sqrt(v*pi) * gamma(v/2)) * (1 + x.^2/v).^(-(v+1)/2);
f_norm = @(x) exp(-x.^2/2) / sqrt(2*pi);
% Define the integration interval and the number of subintervals for approximation
a = -5;
b = 5;
n = 1000;
% Use trapezoid method to approximate the integrals
h = (b-a)/n;
x = linspace(a, b, n+1);
t_trap = h/2 * (f_t(x(1:end-1), 10) + f_t(x(2:end), 10));
norm_trap = h/2 * (f_norm(x(1:end-1)) + f_norm(x(2:end)));
% Use Simpson's composite method to approximate the integrals
x = linspace(a, b, 2*n+1);
h = (b-a)/(2*n);
t_simp = h/3 * (f_t(x(1:2:end-2), 10) + 4*f_t(x(2:2:end-1), 10) + f_t(x(3:2:end), 10));
norm_simp = h/3 * (f_norm(x(1:2:end-2)) + 4*f_norm(x(2:2:end-1)) + f_norm(x(3:2:end)));
% Calculate the exact values of the integrals
t_exact = integral(@(x) f_t(x, 10), -Inf, Inf);
norm_exact = integral(@(x) f_norm(x), -Inf, Inf);
% Compare the approximations with the exact values
fprintf('T-distribution integral:\n');
fprintf('Trapezoid method: %f\n', t_trap);
fprintf('Simpson''s composite method: %f\n', t_simp);
fprintf('Exact value: %f\n', t_exact);
fprintf('\nNormal distribution integral:\n');
fprintf('Trapezoid method: %f\n', norm_trap);
fprintf('Simpson''s composite method: %f\n', norm_simp);
fprintf('Exact value: %f\n', norm_exact);
% Plot the approximations and the exact values
figure;
subplot(2,1,1);
plot(x, f_t(x, 10), 'k', x(1:end-1), t_trap, 'r', x(1:2:end), t_simp, 'b--');
legend('Exact', 'Trapezoid', 'Simpson''s');
title('T-distribution Probability Density Function');
subplot(2,1,2);
plot(x, f_norm(x), 'k', x(1:end-1), norm_trap, 'r', x(1:2:end), norm_simp, 'b--');
legend('Exact', 'Trapezoid', 'Simpson''s');
title('Normal Distribution Probability Density Function');

7 comentarios
Mostrar 5 comentarios más antiguosOcultar 5 comentarios más antiguos

Shoaib Salim el 6 de Abr. de 2023

In plot command i get error of different vector length. How can i change it to get plot similar to exact value of 1

Torsten el 7 de Abr. de 2023

Editada: Torsten el 7 de Abr. de 2023

Didn't you understand what I mean ?

What do you want to plot in case you determine the value of an integral over a predefined interval ?

The only thing I can think of is to plot integral_{t=a}^{t=x} f(t) dt in a given grid point x. But you don't calculate these integrals in your code and you didn't comment on this suggestion I've already done earlier.

Iniciar sesión para comentar.

Iniciar sesión para responder a esta pregunta.

Answer 1

Oguz Kaan Hancioglu el 6 de Abr. de 2023

0
Enlazar

Enlace directo a esta respuesta

https://es.mathworks.com/matlabcentral/answers/1942789-numerical-method-matlab-code#answer_1211064

Abrir en MATLAB Online

The length(x(1:end-1)) and length(t_trap) are not equal. Also, the length(x(1:2:end)) and length(t_simp) are not the equal. I think you can equal the length(x(1:2:end)) and length(t_simp) by changing x(3:2:end). However, the length(x(1:end-1)) is equal twice of length(t_trap).

% Title: Comparison of Trapezoid and Simpson's Composite Methods for T-distribution and Normal Distribution

% Name: TXXXX XXXXXXX

% Class: Scientific Computing

% Define the probability density functions for T-distribution and normal distribution

f_t = @(x, v) gamma((v+1)/2) / (sqrt(v*pi) * gamma(v/2)) * (1 + x.^2/v).^(-(v+1)/2);

f_norm = @(x) exp(-x.^2/2) / sqrt(2*pi);

% Define the integration interval and the number of subintervals for approximation

a = -5;

b = 5;

n = 1000;

% Use trapezoid method to approximate the integrals

h = (b-a)/n;

x = linspace(a, b, n+1);

t_trap = h/2 * (f_t(x(1:end-1), 10) + f_t(x(2:end), 10));

norm_trap = h/2 * (f_norm(x(1:end-1)) + f_norm(x(2:end)));

% Use Simpson's composite method to approximate the integrals

x = linspace(a, b, 2*n+1);

h = (b-a)/(2*n);

t_simp = h/3 * (f_t(x(1:2:end-2), 10) + 4*f_t(x(2:2:end-1), 10) + f_t(x(3:2:end), 10));

norm_simp = h/3 * (f_norm(x(1:2:end-2)) + 4*f_norm(x(2:2:end-1)) + f_norm(x(3:2:end)));

% Calculate the exact values of the integrals

t_exact = integral(@(x) f_t(x, 10), -Inf, Inf);

norm_exact = integral(@(x) f_norm(x), -Inf, Inf);

% Compare the approximations with the exact values

fprintf('T-distribution integral:\n');

T-distribution integral:

fprintf('Trapezoid method: %f\n', t_trap);

Trapezoid method: 0.000004 Trapezoid method: 0.000004 Trapezoid method: 0.000004 Trapezoid method: 0.000004 Trapezoid method: 0.000004 Trapezoid method: 0.000004 Trapezoid method: 0.000004 Trapezoid method: 0.000004 Trapezoid method: 0.000005 Trapezoid method: 0.000005 Trapezoid method: 0.000005 Trapezoid method: 0.000005 Trapezoid method: 0.000005 Trapezoid method: 0.000005 Trapezoid method: 0.000005 Trapezoid method: 0.000005 Trapezoid method: 0.000005 Trapezoid method: 0.000005 Trapezoid method: 0.000005 Trapezoid method: 0.000005 Trapezoid method: 0.000005 Trapezoid method: 0.000006 Trapezoid method: 0.000006 Trapezoid method: 0.000006 Trapezoid method: 0.000006 Trapezoid method: 0.000006 Trapezoid method: 0.000006 Trapezoid method: 0.000006 Trapezoid method: 0.000006 Trapezoid method: 0.000006 Trapezoid method: 0.000006 Trapezoid method: 0.000007 Trapezoid method: 0.000007 Trapezoid method: 0.000007 Trapezoid method: 0.000007 Trapezoid method: 0.000007 Trapezoid method: 0.000007 Trapezoid method: 0.000007 Trapezoid method: 0.000007 Trapezoid method: 0.000007 Trapezoid method: 0.000008 Trapezoid method: 0.000008 Trapezoid method: 0.000008 Trapezoid method: 0.000008 Trapezoid method: 0.000008 Trapezoid method: 0.000008 Trapezoid method: 0.000008 Trapezoid method: 0.000008 Trapezoid method: 0.000009 Trapezoid method: 0.000009 Trapezoid method: 0.000009 Trapezoid method: 0.000009 Trapezoid method: 0.000009 Trapezoid method: 0.000009 Trapezoid method: 0.000010 Trapezoid method: 0.000010 Trapezoid method: 0.000010 Trapezoid method: 0.000010 Trapezoid method: 0.000010 Trapezoid method: 0.000010 Trapezoid method: 0.000010 Trapezoid method: 0.000011 Trapezoid method: 0.000011 Trapezoid method: 0.000011 Trapezoid method: 0.000011 Trapezoid method: 0.000011 Trapezoid method: 0.000012 Trapezoid method: 0.000012 Trapezoid method: 0.000012 Trapezoid method: 0.000012 Trapezoid method: 0.000012 Trapezoid method: 0.000013 Trapezoid method: 0.000013 Trapezoid method: 0.000013 Trapezoid method: 0.000013 Trapezoid method: 0.000013 Trapezoid method: 0.000014 Trapezoid method: 0.000014 Trapezoid method: 0.000014 Trapezoid method: 0.000014 Trapezoid method: 0.000015 Trapezoid method: 0.000015 Trapezoid method: 0.000015 Trapezoid method: 0.000015 Trapezoid method: 0.000016 Trapezoid method: 0.000016 Trapezoid method: 0.000016 Trapezoid method: 0.000016 Trapezoid method: 0.000017 Trapezoid method: 0.000017 Trapezoid method: 0.000017 Trapezoid method: 0.000018 Trapezoid method: 0.000018 Trapezoid method: 0.000018 Trapezoid method: 0.000019 Trapezoid method: 0.000019 Trapezoid method: 0.000019 Trapezoid method: 0.000019 Trapezoid method: 0.000020 Trapezoid method: 0.000020 Trapezoid method: 0.000020 Trapezoid method: 0.000021 Trapezoid method: 0.000021 Trapezoid method: 0.000022 Trapezoid method: 0.000022 Trapezoid method: 0.000022 Trapezoid method: 0.000023 Trapezoid method: 0.000023 Trapezoid method: 0.000023 Trapezoid method: 0.000024 Trapezoid method: 0.000024 Trapezoid method: 0.000025 Trapezoid method: 0.000025 Trapezoid method: 0.000026 Trapezoid method: 0.000026 Trapezoid method: 0.000026 Trapezoid method: 0.000027 Trapezoid method: 0.000027 Trapezoid method: 0.000028 Trapezoid method: 0.000028 Trapezoid method: 0.000029 Trapezoid method: 0.000029 Trapezoid method: 0.000030 Trapezoid method: 0.000030 Trapezoid method: 0.000031 Trapezoid method: 0.000031 Trapezoid method: 0.000032 Trapezoid method: 0.000032 Trapezoid method: 0.000033 Trapezoid method: 0.000034 Trapezoid method: 0.000034 Trapezoid method: 0.000035 Trapezoid method: 0.000035 Trapezoid method: 0.000036 Trapezoid method: 0.000037 Trapezoid method: 0.000037 Trapezoid method: 0.000038 Trapezoid method: 0.000039 Trapezoid method: 0.000039 Trapezoid method: 0.000040 Trapezoid method: 0.000041 Trapezoid method: 0.000041 Trapezoid method: 0.000042 Trapezoid method: 0.000043 Trapezoid method: 0.000043 Trapezoid method: 0.000044 Trapezoid method: 0.000045 Trapezoid method: 0.000046 Trapezoid method: 0.000047 Trapezoid method: 0.000047 Trapezoid method: 0.000048 Trapezoid method: 0.000049 Trapezoid method: 0.000050 Trapezoid method: 0.000051 Trapezoid method: 0.000052 Trapezoid method: 0.000053 Trapezoid method: 0.000054 Trapezoid method: 0.000054 Trapezoid method: 0.000055 Trapezoid method: 0.000056 Trapezoid method: 0.000057 Trapezoid method: 0.000058 Trapezoid method: 0.000059 Trapezoid method: 0.000060 Trapezoid method: 0.000062 Trapezoid method: 0.000063 Trapezoid method: 0.000064 Trapezoid method: 0.000065 Trapezoid method: 0.000066 Trapezoid method: 0.000067 Trapezoid method: 0.000068 Trapezoid method: 0.000069 Trapezoid method: 0.000071 Trapezoid method: 0.000072 Trapezoid method: 0.000073 Trapezoid method: 0.000074 Trapezoid method: 0.000076 Trapezoid method: 0.000077 Trapezoid method: 0.000078 Trapezoid method: 0.000080 Trapezoid method: 0.000081 Trapezoid method: 0.000083 Trapezoid method: 0.000084 Trapezoid method: 0.000086 Trapezoid method: 0.000087 Trapezoid method: 0.000089 Trapezoid method: 0.000090 Trapezoid method: 0.000092 Trapezoid method: 0.000093 Trapezoid method: 0.000095 Trapezoid method: 0.000097 Trapezoid method: 0.000098 Trapezoid method: 0.000100 Trapezoid method: 0.000102 Trapezoid method: 0.000104 Trapezoid method: 0.000105 Trapezoid method: 0.000107 Trapezoid method: 0.000109 Trapezoid method: 0.000111 Trapezoid method: 0.000113 Trapezoid method: 0.000115 Trapezoid method: 0.000117 Trapezoid method: 0.000119 Trapezoid method: 0.000121 Trapezoid method: 0.000123 Trapezoid method: 0.000125 Trapezoid method: 0.000128 Trapezoid method: 0.000130 Trapezoid method: 0.000132 Trapezoid method: 0.000134 Trapezoid method: 0.000137 Trapezoid method: 0.000139 Trapezoid method: 0.000142 Trapezoid method: 0.000144 Trapezoid method: 0.000147 Trapezoid method: 0.000149 Trapezoid method: 0.000152 Trapezoid method: 0.000154 Trapezoid method: 0.000157 Trapezoid method: 0.000160 Trapezoid method: 0.000163 Trapezoid method: 0.000165 Trapezoid method: 0.000168 Trapezoid method: 0.000171 Trapezoid method: 0.000174 Trapezoid method: 0.000177 Trapezoid method: 0.000180 Trapezoid method: 0.000183 Trapezoid method: 0.000187 Trapezoid method: 0.000190 Trapezoid method: 0.000193 Trapezoid method: 0.000197 Trapezoid method: 0.000200 Trapezoid method: 0.000203 Trapezoid method: 0.000207 Trapezoid method: 0.000210 Trapezoid method: 0.000214 Trapezoid method: 0.000218 Trapezoid method: 0.000222 Trapezoid method: 0.000225 Trapezoid method: 0.000229 Trapezoid method: 0.000233 Trapezoid method: 0.000237 Trapezoid method: 0.000241 Trapezoid method: 0.000245 Trapezoid method: 0.000250 Trapezoid method: 0.000254 Trapezoid method: 0.000258 Trapezoid method: 0.000263 Trapezoid method: 0.000267 Trapezoid method: 0.000272 Trapezoid method: 0.000276 Trapezoid method: 0.000281 Trapezoid method: 0.000286 Trapezoid method: 0.000291 Trapezoid method: 0.000296 Trapezoid method: 0.000301 Trapezoid method: 0.000306 Trapezoid method: 0.000311 Trapezoid method: 0.000316 Trapezoid method: 0.000321 Trapezoid method: 0.000327 Trapezoid method: 0.000332 Trapezoid method: 0.000338 Trapezoid method: 0.000344 Trapezoid method: 0.000349 Trapezoid method: 0.000355 Trapezoid method: 0.000361 Trapezoid method: 0.000367 Trapezoid method: 0.000373 Trapezoid method: 0.000380 Trapezoid method: 0.000386 Trapezoid method: 0.000392 Trapezoid method: 0.000399 Trapezoid method: 0.000406 Trapezoid method: 0.000412 Trapezoid method: 0.000419 Trapezoid method: 0.000426 Trapezoid method: 0.000433 Trapezoid method: 0.000440 Trapezoid method: 0.000447 Trapezoid method: 0.000455 Trapezoid method: 0.000462 Trapezoid method: 0.000470 Trapezoid method: 0.000477 Trapezoid method: 0.000485 Trapezoid method: 0.000493 Trapezoid method: 0.000501 Trapezoid method: 0.000509 Trapezoid method: 0.000518 Trapezoid method: 0.000526 Trapezoid method: 0.000534 Trapezoid method: 0.000543 Trapezoid method: 0.000552 Trapezoid method: 0.000561 Trapezoid method: 0.000570 Trapezoid method: 0.000579 Trapezoid method: 0.000588 Trapezoid method: 0.000597 Trapezoid method: 0.000607 Trapezoid method: 0.000616 Trapezoid method: 0.000626 Trapezoid method: 0.000636 Trapezoid method: 0.000646 Trapezoid method: 0.000656 Trapezoid method: 0.000666 Trapezoid method: 0.000677 Trapezoid method: 0.000687 Trapezoid method: 0.000698 Trapezoid method: 0.000709 Trapezoid method: 0.000720 Trapezoid method: 0.000731 Trapezoid method: 0.000742 Trapezoid method: 0.000754 Trapezoid method: 0.000765 Trapezoid method: 0.000777 Trapezoid method: 0.000789 Trapezoid method: 0.000801 Trapezoid method: 0.000813 Trapezoid method: 0.000825 Trapezoid method: 0.000837 Trapezoid method: 0.000850 Trapezoid method: 0.000863 Trapezoid method: 0.000876 Trapezoid method: 0.000889 Trapezoid method: 0.000902 Trapezoid method: 0.000915 Trapezoid method: 0.000929 Trapezoid method: 0.000942 Trapezoid method: 0.000956 Trapezoid method: 0.000970 Trapezoid method: 0.000984 Trapezoid method: 0.000999 Trapezoid method: 0.001013 Trapezoid method: 0.001028 Trapezoid method: 0.001042 Trapezoid method: 0.001057 Trapezoid method: 0.001072 Trapezoid method: 0.001088 Trapezoid method: 0.001103 Trapezoid method: 0.001119 Trapezoid method: 0.001134 Trapezoid method: 0.001150 Trapezoid method: 0.001166 Trapezoid method: 0.001182 Trapezoid method: 0.001199 Trapezoid method: 0.001215 Trapezoid method: 0.001232 Trapezoid method: 0.001249 Trapezoid method: 0.001266 Trapezoid method: 0.001283 Trapezoid method: 0.001300 Trapezoid method: 0.001318 Trapezoid method: 0.001336 Trapezoid method: 0.001353 Trapezoid method: 0.001371 Trapezoid method: 0.001389 Trapezoid method: 0.001408 Trapezoid method: 0.001426 Trapezoid method: 0.001445 Trapezoid method: 0.001463 Trapezoid method: 0.001482 Trapezoid method: 0.001501 Trapezoid method: 0.001520 Trapezoid method: 0.001540 Trapezoid method: 0.001559 Trapezoid method: 0.001579 Trapezoid method: 0.001599 Trapezoid method: 0.001618 Trapezoid method: 0.001638 Trapezoid method: 0.001659 Trapezoid method: 0.001679 Trapezoid method: 0.001699 Trapezoid method: 0.001720 Trapezoid method: 0.001741 Trapezoid method: 0.001761 Trapezoid method: 0.001782 Trapezoid method: 0.001803 Trapezoid method: 0.001825 Trapezoid method: 0.001846 Trapezoid method: 0.001867 Trapezoid method: 0.001889 Trapezoid method: 0.001911 Trapezoid method: 0.001932 Trapezoid method: 0.001954 Trapezoid method: 0.001976 Trapezoid method: 0.001998 Trapezoid method: 0.002020 Trapezoid method: 0.002043 Trapezoid method: 0.002065 Trapezoid method: 0.002087 Trapezoid method: 0.002110 Trapezoid method: 0.002132 Trapezoid method: 0.002155 Trapezoid method: 0.002178 Trapezoid method: 0.002200 Trapezoid method: 0.002223 Trapezoid method: 0.002246 Trapezoid method: 0.002269 Trapezoid method: 0.002292 Trapezoid method: 0.002315 Trapezoid method: 0.002338 Trapezoid method: 0.002361 Trapezoid method: 0.002384 Trapezoid method: 0.002408 Trapezoid method: 0.002431 Trapezoid method: 0.002454 Trapezoid method: 0.002477 Trapezoid method: 0.002500 Trapezoid method: 0.002524 Trapezoid method: 0.002547 Trapezoid method: 0.002570 Trapezoid method: 0.002593 Trapezoid method: 0.002616 Trapezoid method: 0.002640 Trapezoid method: 0.002663 Trapezoid method: 0.002686 Trapezoid method: 0.002709 Trapezoid method: 0.002732 Trapezoid method: 0.002755 Trapezoid method: 0.002778 Trapezoid method: 0.002800 Trapezoid method: 0.002823 Trapezoid method: 0.002846 Trapezoid method: 0.002868 Trapezoid method: 0.002891 Trapezoid method: 0.002913 Trapezoid method: 0.002936 Trapezoid method: 0.002958 Trapezoid method: 0.002980 Trapezoid method: 0.003002 Trapezoid method: 0.003024 Trapezoid method: 0.003045 Trapezoid method: 0.003067 Trapezoid method: 0.003088 Trapezoid method: 0.003110 Trapezoid method: 0.003131 Trapezoid method: 0.003152 Trapezoid method: 0.003172 Trapezoid method: 0.003193 Trapezoid method: 0.003213 Trapezoid method: 0.003234 Trapezoid method: 0.003254 Trapezoid method: 0.003273 Trapezoid method: 0.003293 Trapezoid method: 0.003312 Trapezoid method: 0.003332 Trapezoid method: 0.003351 Trapezoid method: 0.003369 Trapezoid method: 0.003388 Trapezoid method: 0.003406 Trapezoid method: 0.003424 Trapezoid method: 0.003442 Trapezoid method: 0.003459 Trapezoid method: 0.003476 Trapezoid method: 0.003493 Trapezoid method: 0.003510 Trapezoid method: 0.003526 Trapezoid method: 0.003542 Trapezoid method: 0.003558 Trapezoid method: 0.003573 Trapezoid method: 0.003589 Trapezoid method: 0.003603 Trapezoid method: 0.003618 Trapezoid method: 0.003632 Trapezoid method: 0.003646 Trapezoid method: 0.003659 Trapezoid method: 0.003673 Trapezoid method: 0.003685 Trapezoid method: 0.003698 Trapezoid method: 0.003710 Trapezoid method: 0.003722 Trapezoid method: 0.003733 Trapezoid method: 0.003744 Trapezoid method: 0.003755 Trapezoid method: 0.003765 Trapezoid method: 0.003775 Trapezoid method: 0.003784 Trapezoid method: 0.003794 Trapezoid method: 0.003802 Trapezoid method: 0.003811 Trapezoid method: 0.003819 Trapezoid method: 0.003826 Trapezoid method: 0.003833 Trapezoid method: 0.003840 Trapezoid method: 0.003846 Trapezoid method: 0.003852 Trapezoid method: 0.003858 Trapezoid method: 0.003863 Trapezoid method: 0.003868 Trapezoid method: 0.003872 Trapezoid method: 0.003876 Trapezoid method: 0.003879 Trapezoid method: 0.003882 Trapezoid method: 0.003885 Trapezoid method: 0.003887 Trapezoid method: 0.003888 Trapezoid method: 0.003890 Trapezoid method: 0.003891 Trapezoid method: 0.003891 Trapezoid method: 0.003891 Trapezoid method: 0.003891 Trapezoid method: 0.003890 Trapezoid method: 0.003888 Trapezoid method: 0.003887 Trapezoid method: 0.003885 Trapezoid method: 0.003882 Trapezoid method: 0.003879 Trapezoid method: 0.003876 Trapezoid method: 0.003872 Trapezoid method: 0.003868 Trapezoid method: 0.003863 Trapezoid method: 0.003858 Trapezoid method: 0.003852 Trapezoid method: 0.003846 Trapezoid method: 0.003840 Trapezoid method: 0.003833 Trapezoid method: 0.003826 Trapezoid method: 0.003819 Trapezoid method: 0.003811 Trapezoid method: 0.003802 Trapezoid method: 0.003794 Trapezoid method: 0.003784 Trapezoid method: 0.003775 Trapezoid method: 0.003765 Trapezoid method: 0.003755 Trapezoid method: 0.003744 Trapezoid method: 0.003733 Trapezoid method: 0.003722 Trapezoid method: 0.003710 Trapezoid method: 0.003698 Trapezoid method: 0.003685 Trapezoid method: 0.003673 Trapezoid method: 0.003659 Trapezoid method: 0.003646 Trapezoid method: 0.003632 Trapezoid method: 0.003618 Trapezoid method: 0.003603 Trapezoid method: 0.003589 Trapezoid method: 0.003573 Trapezoid method: 0.003558 Trapezoid method: 0.003542 Trapezoid method: 0.003526 Trapezoid method: 0.003510 Trapezoid method: 0.003493 Trapezoid method: 0.003476 Trapezoid method: 0.003459 Trapezoid method: 0.003442 Trapezoid method: 0.003424 Trapezoid method: 0.003406 Trapezoid method: 0.003388 Trapezoid method: 0.003369 Trapezoid method: 0.003351 Trapezoid method: 0.003332 Trapezoid method: 0.003312 Trapezoid method: 0.003293 Trapezoid method: 0.003273 Trapezoid method: 0.003254 Trapezoid method: 0.003234 Trapezoid method: 0.003213 Trapezoid method: 0.003193 Trapezoid method: 0.003172 Trapezoid method: 0.003152 Trapezoid method: 0.003131 Trapezoid method: 0.003110 Trapezoid method: 0.003088 Trapezoid method: 0.003067 Trapezoid method: 0.003045 Trapezoid method: 0.003024 Trapezoid method: 0.003002 Trapezoid method: 0.002980 Trapezoid method: 0.002958 Trapezoid method: 0.002936 Trapezoid method: 0.002913 Trapezoid method: 0.002891 Trapezoid method: 0.002868 Trapezoid method: 0.002846 Trapezoid method: 0.002823 Trapezoid method: 0.002800 Trapezoid method: 0.002778 Trapezoid method: 0.002755 Trapezoid method: 0.002732 Trapezoid method: 0.002709 Trapezoid method: 0.002686 Trapezoid method: 0.002663 Trapezoid method: 0.002640 Trapezoid method: 0.002616 Trapezoid method: 0.002593 Trapezoid method: 0.002570 Trapezoid method: 0.002547 Trapezoid method: 0.002524 Trapezoid method: 0.002500 Trapezoid method: 0.002477 Trapezoid method: 0.002454 Trapezoid method: 0.002431 Trapezoid method: 0.002408 Trapezoid method: 0.002384 Trapezoid method: 0.002361 Trapezoid method: 0.002338 Trapezoid method: 0.002315 Trapezoid method: 0.002292 Trapezoid method: 0.002269 Trapezoid method: 0.002246 Trapezoid method: 0.002223 Trapezoid method: 0.002200 Trapezoid method: 0.002178 Trapezoid method: 0.002155 Trapezoid method: 0.002132 Trapezoid method: 0.002110 Trapezoid method: 0.002087 Trapezoid method: 0.002065 Trapezoid method: 0.002043 Trapezoid method: 0.002020 Trapezoid method: 0.001998 Trapezoid method: 0.001976 Trapezoid method: 0.001954 Trapezoid method: 0.001932 Trapezoid method: 0.001911 Trapezoid method: 0.001889 Trapezoid method: 0.001867 Trapezoid method: 0.001846 Trapezoid method: 0.001825 Trapezoid method: 0.001803 Trapezoid method: 0.001782 Trapezoid method: 0.001761 Trapezoid method: 0.001741 Trapezoid method: 0.001720 Trapezoid method: 0.001699 Trapezoid method: 0.001679 Trapezoid method: 0.001659 Trapezoid method: 0.001638 Trapezoid method: 0.001618 Trapezoid method: 0.001599 Trapezoid method: 0.001579 Trapezoid method: 0.001559 Trapezoid method: 0.001540 Trapezoid method: 0.001520 Trapezoid method: 0.001501 Trapezoid method: 0.001482 Trapezoid method: 0.001463 Trapezoid method: 0.001445 Trapezoid method: 0.001426 Trapezoid method: 0.001408 Trapezoid method: 0.001389 Trapezoid method: 0.001371 Trapezoid method: 0.001353 Trapezoid method: 0.001336 Trapezoid method: 0.001318 Trapezoid method: 0.001300 Trapezoid method: 0.001283 Trapezoid method: 0.001266 Trapezoid method: 0.001249 Trapezoid method: 0.001232 Trapezoid method: 0.001215 Trapezoid method: 0.001199 Trapezoid method: 0.001182 Trapezoid method: 0.001166 Trapezoid method: 0.001150 Trapezoid method: 0.001134 Trapezoid method: 0.001119 Trapezoid method: 0.001103 Trapezoid method: 0.001088 Trapezoid method: 0.001072 Trapezoid method: 0.001057 Trapezoid method: 0.001042 Trapezoid method: 0.001028 Trapezoid method: 0.001013 Trapezoid method: 0.000999 Trapezoid method: 0.000984 Trapezoid method: 0.000970 Trapezoid method: 0.000956 Trapezoid method: 0.000942 Trapezoid method: 0.000929 Trapezoid method: 0.000915 Trapezoid method: 0.000902 Trapezoid method: 0.000889 Trapezoid method: 0.000876 Trapezoid method: 0.000863 Trapezoid method: 0.000850 Trapezoid method: 0.000837 Trapezoid method: 0.000825 Trapezoid method: 0.000813 Trapezoid method: 0.000801 Trapezoid method: 0.000789 Trapezoid method: 0.000777 Trapezoid method: 0.000765 Trapezoid method: 0.000754 Trapezoid method: 0.000742 Trapezoid method: 0.000731 Trapezoid method: 0.000720 Trapezoid method: 0.000709 Trapezoid method: 0.000698 Trapezoid method: 0.000687 Trapezoid method: 0.000677 Trapezoid method: 0.000666 Trapezoid method: 0.000656 Trapezoid method: 0.000646 Trapezoid method: 0.000636 Trapezoid method: 0.000626 Trapezoid method: 0.000616 Trapezoid method: 0.000607 Trapezoid method: 0.000597 Trapezoid method: 0.000588 Trapezoid method: 0.000579 Trapezoid method: 0.000570 Trapezoid method: 0.000561 Trapezoid method: 0.000552 Trapezoid method: 0.000543 Trapezoid method: 0.000534 Trapezoid method: 0.000526 Trapezoid method: 0.000518 Trapezoid method: 0.000509 Trapezoid method: 0.000501 Trapezoid method: 0.000493 Trapezoid method: 0.000485 Trapezoid method: 0.000477 Trapezoid method: 0.000470 Trapezoid method: 0.000462 Trapezoid method: 0.000455 Trapezoid method: 0.000447 Trapezoid method: 0.000440 Trapezoid method: 0.000433 Trapezoid method: 0.000426 Trapezoid method: 0.000419 Trapezoid method: 0.000412 Trapezoid method: 0.000406 Trapezoid method: 0.000399 Trapezoid method: 0.000392 Trapezoid method: 0.000386 Trapezoid method: 0.000380 Trapezoid method: 0.000373 Trapezoid method: 0.000367 Trapezoid method: 0.000361 Trapezoid method: 0.000355 Trapezoid method: 0.000349 Trapezoid method: 0.000344 Trapezoid method: 0.000338 Trapezoid method: 0.000332 Trapezoid method: 0.000327 Trapezoid method: 0.000321 Trapezoid method: 0.000316 Trapezoid method: 0.000311 Trapezoid method: 0.000306 Trapezoid method: 0.000301 Trapezoid method: 0.000296 Trapezoid method: 0.000291 Trapezoid method: 0.000286 Trapezoid method: 0.000281 Trapezoid method: 0.000276 Trapezoid method: 0.000272 Trapezoid method: 0.000267 Trapezoid method: 0.000263 Trapezoid method: 0.000258 Trapezoid method: 0.000254 Trapezoid method: 0.000250 Trapezoid method: 0.000245 Trapezoid method: 0.000241 Trapezoid method: 0.000237 Trapezoid method: 0.000233 Trapezoid method: 0.000229 Trapezoid method: 0.000225 Trapezoid method: 0.000222 Trapezoid method: 0.000218 Trapezoid method: 0.000214 Trapezoid method: 0.000210 Trapezoid method: 0.000207 Trapezoid method: 0.000203 Trapezoid method: 0.000200 Trapezoid method: 0.000197 Trapezoid method: 0.000193 Trapezoid method: 0.000190 Trapezoid method: 0.000187 Trapezoid method: 0.000183 Trapezoid method: 0.000180 Trapezoid method: 0.000177 Trapezoid method: 0.000174 Trapezoid method: 0.000171 Trapezoid method: 0.000168 Trapezoid method: 0.000165 Trapezoid method: 0.000163 Trapezoid method: 0.000160 Trapezoid method: 0.000157 Trapezoid method: 0.000154 Trapezoid method: 0.000152 Trapezoid method: 0.000149 Trapezoid method: 0.000147 Trapezoid method: 0.000144 Trapezoid method: 0.000142 Trapezoid method: 0.000139 Trapezoid method: 0.000137 Trapezoid method: 0.000134 Trapezoid method: 0.000132 Trapezoid method: 0.000130 Trapezoid method: 0.000128 Trapezoid method: 0.000125 Trapezoid method: 0.000123 Trapezoid method: 0.000121 Trapezoid method: 0.000119 Trapezoid method: 0.000117 Trapezoid method: 0.000115 Trapezoid method: 0.000113 Trapezoid method: 0.000111 Trapezoid method: 0.000109 Trapezoid method: 0.000107 Trapezoid method: 0.000105 Trapezoid method: 0.000104 Trapezoid method: 0.000102 Trapezoid method: 0.000100 Trapezoid method: 0.000098 Trapezoid method: 0.000097 Trapezoid method: 0.000095 Trapezoid method: 0.000093 Trapezoid method: 0.000092 Trapezoid method: 0.000090 Trapezoid method: 0.000089 Trapezoid method: 0.000087 Trapezoid method: 0.000086 Trapezoid method: 0.000084 Trapezoid method: 0.000083 Trapezoid method: 0.000081 Trapezoid method: 0.000080 Trapezoid method: 0.000078 Trapezoid method: 0.000077 Trapezoid method: 0.000076 Trapezoid method: 0.000074 Trapezoid method: 0.000073 Trapezoid method: 0.000072 Trapezoid method: 0.000071 Trapezoid method: 0.000069 Trapezoid method: 0.000068 Trapezoid method: 0.000067 Trapezoid method: 0.000066 Trapezoid method: 0.000065 Trapezoid method: 0.000064 Trapezoid method: 0.000063 Trapezoid method: 0.000062 Trapezoid method: 0.000060 Trapezoid method: 0.000059 Trapezoid method: 0.000058 Trapezoid method: 0.000057 Trapezoid method: 0.000056 Trapezoid method: 0.000055 Trapezoid method: 0.000054 Trapezoid method: 0.000054 Trapezoid method: 0.000053 Trapezoid method: 0.000052 Trapezoid method: 0.000051 Trapezoid method: 0.000050 Trapezoid method: 0.000049 Trapezoid method: 0.000048 Trapezoid method: 0.000047 Trapezoid method: 0.000047 Trapezoid method: 0.000046 Trapezoid method: 0.000045 Trapezoid method: 0.000044 Trapezoid method: 0.000043 Trapezoid method: 0.000043 Trapezoid method: 0.000042 Trapezoid method: 0.000041 Trapezoid method: 0.000041 Trapezoid method: 0.000040 Trapezoid method: 0.000039 Trapezoid method: 0.000039 Trapezoid method: 0.000038 Trapezoid method: 0.000037 Trapezoid method: 0.000037 Trapezoid method: 0.000036 Trapezoid method: 0.000035 Trapezoid method: 0.000035 Trapezoid method: 0.000034 Trapezoid method: 0.000034 Trapezoid method: 0.000033 Trapezoid method: 0.000032 Trapezoid method: 0.000032 Trapezoid method: 0.000031 Trapezoid method: 0.000031 Trapezoid method: 0.000030 Trapezoid method: 0.000030 Trapezoid method: 0.000029 Trapezoid method: 0.000029 Trapezoid method: 0.000028 Trapezoid method: 0.000028 Trapezoid method: 0.000027 Trapezoid method: 0.000027 Trapezoid method: 0.000026 Trapezoid method: 0.000026 Trapezoid method: 0.000026 Trapezoid method: 0.000025 Trapezoid method: 0.000025 Trapezoid method: 0.000024 Trapezoid method: 0.000024 Trapezoid method: 0.000023 Trapezoid method: 0.000023 Trapezoid method: 0.000023 Trapezoid method: 0.000022 Trapezoid method: 0.000022 Trapezoid method: 0.000022 Trapezoid method: 0.000021 Trapezoid method: 0.000021 Trapezoid method: 0.000020 Trapezoid method: 0.000020 Trapezoid method: 0.000020 Trapezoid method: 0.000019 Trapezoid method: 0.000019 Trapezoid method: 0.000019 Trapezoid method: 0.000019 Trapezoid method: 0.000018 Trapezoid method: 0.000018 Trapezoid method: 0.000018 Trapezoid method: 0.000017 Trapezoid method: 0.000017 Trapezoid method: 0.000017 Trapezoid method: 0.000016 Trapezoid method: 0.000016 Trapezoid method: 0.000016 Trapezoid method: 0.000016 Trapezoid method: 0.000015 Trapezoid method: 0.000015 Trapezoid method: 0.000015 Trapezoid method: 0.000015 Trapezoid method: 0.000014 Trapezoid method: 0.000014 Trapezoid method: 0.000014 Trapezoid method: 0.000014 Trapezoid method: 0.000013 Trapezoid method: 0.000013 Trapezoid method: 0.000013 Trapezoid method: 0.000013 Trapezoid method: 0.000013 Trapezoid method: 0.000012 Trapezoid method: 0.000012 Trapezoid method: 0.000012 Trapezoid method: 0.000012 Trapezoid method: 0.000012 Trapezoid method: 0.000011 Trapezoid method: 0.000011 Trapezoid method: 0.000011 Trapezoid method: 0.000011 Trapezoid method: 0.000011 Trapezoid method: 0.000010 Trapezoid method: 0.000010 Trapezoid method: 0.000010 Trapezoid method: 0.000010 Trapezoid method: 0.000010 Trapezoid method: 0.000010 Trapezoid method: 0.000010 Trapezoid method: 0.000009 Trapezoid method: 0.000009 Trapezoid method: 0.000009 Trapezoid method: 0.000009 Trapezoid method: 0.000009 Trapezoid method: 0.000009 Trapezoid method: 0.000008 Trapezoid method: 0.000008 Trapezoid method: 0.000008 Trapezoid method: 0.000008 Trapezoid method: 0.000008 Trapezoid method: 0.000008 Trapezoid method: 0.000008 Trapezoid method: 0.000008 Trapezoid method: 0.000007 Trapezoid method: 0.000007 Trapezoid method: 0.000007 Trapezoid method: 0.000007 Trapezoid method: 0.000007 Trapezoid method: 0.000007 Trapezoid method: 0.000007 Trapezoid method: 0.000007 Trapezoid method: 0.000007 Trapezoid method: 0.000006 Trapezoid method: 0.000006 Trapezoid method: 0.000006 Trapezoid method: 0.000006 Trapezoid method: 0.000006 Trapezoid method: 0.000006 Trapezoid method: 0.000006 Trapezoid method: 0.000006 Trapezoid method: 0.000006 Trapezoid method: 0.000006 Trapezoid method: 0.000005 Trapezoid method: 0.000005 Trapezoid method: 0.000005 Trapezoid method: 0.000005 Trapezoid method: 0.000005 Trapezoid method: 0.000005 Trapezoid method: 0.000005 Trapezoid method: 0.000005 Trapezoid method: 0.000005 Trapezoid method: 0.000005 Trapezoid method: 0.000005 Trapezoid method: 0.000005 Trapezoid method: 0.000005 Trapezoid method: 0.000004 Trapezoid method: 0.000004 Trapezoid method: 0.000004 Trapezoid method: 0.000004 Trapezoid method: 0.000004 Trapezoid method: 0.000004 Trapezoid method: 0.000004 Trapezoid method: 0.000004

fprintf('Simpson''s composite method: %f\n', t_simp);

Simpson's composite method: 0.000004 Simpson's composite method: 0.000004 Simpson's composite method: 0.000004 Simpson's composite method: 0.000004 Simpson's composite method: 0.000004 Simpson's composite method: 0.000004 Simpson's composite method: 0.000004 Simpson's composite method: 0.000004 Simpson's composite method: 0.000005 Simpson's composite method: 0.000005 Simpson's composite method: 0.000005 Simpson's composite method: 0.000005 Simpson's composite method: 0.000005 Simpson's composite method: 0.000005 Simpson's composite method: 0.000005 Simpson's composite method: 0.000005 Simpson's composite method: 0.000005 Simpson's composite method: 0.000005 Simpson's composite method: 0.000005 Simpson's composite method: 0.000005 Simpson's composite method: 0.000005 Simpson's composite method: 0.000006 Simpson's composite method: 0.000006 Simpson's composite method: 0.000006 Simpson's composite method: 0.000006 Simpson's composite method: 0.000006 Simpson's composite method: 0.000006 Simpson's composite method: 0.000006 Simpson's composite method: 0.000006 Simpson's composite method: 0.000006 Simpson's composite method: 0.000006 Simpson's composite method: 0.000007 Simpson's composite method: 0.000007 Simpson's composite method: 0.000007 Simpson's composite method: 0.000007 Simpson's composite method: 0.000007 Simpson's composite method: 0.000007 Simpson's composite method: 0.000007 Simpson's composite method: 0.000007 Simpson's composite method: 0.000007 Simpson's composite method: 0.000008 Simpson's composite method: 0.000008 Simpson's composite method: 0.000008 Simpson's composite method: 0.000008 Simpson's composite method: 0.000008 Simpson's composite method: 0.000008 Simpson's composite method: 0.000008 Simpson's composite method: 0.000008 Simpson's composite method: 0.000009 Simpson's composite method: 0.000009 Simpson's composite method: 0.000009 Simpson's composite method: 0.000009 Simpson's composite method: 0.000009 Simpson's composite method: 0.000009 Simpson's composite method: 0.000010 Simpson's composite method: 0.000010 Simpson's composite method: 0.000010 Simpson's composite method: 0.000010 Simpson's composite method: 0.000010 Simpson's composite method: 0.000010 Simpson's composite method: 0.000010 Simpson's composite method: 0.000011 Simpson's composite method: 0.000011 Simpson's composite method: 0.000011 Simpson's composite method: 0.000011 Simpson's composite method: 0.000011 Simpson's composite method: 0.000012 Simpson's composite method: 0.000012 Simpson's composite method: 0.000012 Simpson's composite method: 0.000012 Simpson's composite method: 0.000012 Simpson's composite method: 0.000013 Simpson's composite method: 0.000013 Simpson's composite method: 0.000013 Simpson's composite method: 0.000013 Simpson's composite method: 0.000013 Simpson's composite method: 0.000014 Simpson's composite method: 0.000014 Simpson's composite method: 0.000014 Simpson's composite method: 0.000014 Simpson's composite method: 0.000015 Simpson's composite method: 0.000015 Simpson's composite method: 0.000015 Simpson's composite method: 0.000015 Simpson's composite method: 0.000016 Simpson's composite method: 0.000016 Simpson's composite method: 0.000016 Simpson's composite method: 0.000016 Simpson's composite method: 0.000017 Simpson's composite method: 0.000017 Simpson's composite method: 0.000017 Simpson's composite method: 0.000018 Simpson's composite method: 0.000018 Simpson's composite method: 0.000018 Simpson's composite method: 0.000019 Simpson's composite method: 0.000019 Simpson's composite method: 0.000019 Simpson's composite method: 0.000019 Simpson's composite method: 0.000020 Simpson's composite method: 0.000020 Simpson's composite method: 0.000020 Simpson's composite method: 0.000021 Simpson's composite method: 0.000021 Simpson's composite method: 0.000022 Simpson's composite method: 0.000022 Simpson's composite method: 0.000022 Simpson's composite method: 0.000023 Simpson's composite method: 0.000023 Simpson's composite method: 0.000023 Simpson's composite method: 0.000024 Simpson's composite method: 0.000024 Simpson's composite method: 0.000025 Simpson's composite method: 0.000025 Simpson's composite method: 0.000026 Simpson's composite method: 0.000026 Simpson's composite method: 0.000026 Simpson's composite method: 0.000027 Simpson's composite method: 0.000027 Simpson's composite method: 0.000028 Simpson's composite method: 0.000028 Simpson's composite method: 0.000029 Simpson's composite method: 0.000029 Simpson's composite method: 0.000030 Simpson's composite method: 0.000030 Simpson's composite method: 0.000031 Simpson's composite method: 0.000031 Simpson's composite method: 0.000032 Simpson's composite method: 0.000032 Simpson's composite method: 0.000033 Simpson's composite method: 0.000034 Simpson's composite method: 0.000034 Simpson's composite method: 0.000035 Simpson's composite method: 0.000035 Simpson's composite method: 0.000036 Simpson's composite method: 0.000037 Simpson's composite method: 0.000037 Simpson's composite method: 0.000038 Simpson's composite method: 0.000039 Simpson's composite method: 0.000039 Simpson's composite method: 0.000040 Simpson's composite method: 0.000041 Simpson's composite method: 0.000041 Simpson's composite method: 0.000042 Simpson's composite method: 0.000043 Simpson's composite method: 0.000043 Simpson's composite method: 0.000044 Simpson's composite method: 0.000045 Simpson's composite method: 0.000046 Simpson's composite method: 0.000047 Simpson's composite method: 0.000047 Simpson's composite method: 0.000048 Simpson's composite method: 0.000049 Simpson's composite method: 0.000050 Simpson's composite method: 0.000051 Simpson's composite method: 0.000052 Simpson's composite method: 0.000053 Simpson's composite method: 0.000054 Simpson's composite method: 0.000054 Simpson's composite method: 0.000055 Simpson's composite method: 0.000056 Simpson's composite method: 0.000057 Simpson's composite method: 0.000058 Simpson's composite method: 0.000059 Simpson's composite method: 0.000060 Simpson's composite method: 0.000062 Simpson's composite method: 0.000063 Simpson's composite method: 0.000064 Simpson's composite method: 0.000065 Simpson's composite method: 0.000066 Simpson's composite method: 0.000067 Simpson's composite method: 0.000068 Simpson's composite method: 0.000069 Simpson's composite method: 0.000071 Simpson's composite method: 0.000072 Simpson's composite method: 0.000073 Simpson's composite method: 0.000074 Simpson's composite method: 0.000076 Simpson's composite method: 0.000077 Simpson's composite method: 0.000078 Simpson's composite method: 0.000080 Simpson's composite method: 0.000081 Simpson's composite method: 0.000083 Simpson's composite method: 0.000084 Simpson's composite method: 0.000086 Simpson's composite method: 0.000087 Simpson's composite method: 0.000089 Simpson's composite method: 0.000090 Simpson's composite method: 0.000092 Simpson's composite method: 0.000093 Simpson's composite method: 0.000095 Simpson's composite method: 0.000097 Simpson's composite method: 0.000098 Simpson's composite method: 0.000100 Simpson's composite method: 0.000102 Simpson's composite method: 0.000104 Simpson's composite method: 0.000105 Simpson's composite method: 0.000107 Simpson's composite method: 0.000109 Simpson's composite method: 0.000111 Simpson's composite method: 0.000113 Simpson's composite method: 0.000115 Simpson's composite method: 0.000117 Simpson's composite method: 0.000119 Simpson's composite method: 0.000121 Simpson's composite method: 0.000123 Simpson's composite method: 0.000125 Simpson's composite method: 0.000128 Simpson's composite method: 0.000130 Simpson's composite method: 0.000132 Simpson's composite method: 0.000134 Simpson's composite method: 0.000137 Simpson's composite method: 0.000139 Simpson's composite method: 0.000142 Simpson's composite method: 0.000144 Simpson's composite method: 0.000147 Simpson's composite method: 0.000149 Simpson's composite method: 0.000152 Simpson's composite method: 0.000154 Simpson's composite method: 0.000157 Simpson's composite method: 0.000160 Simpson's composite method: 0.000163 Simpson's composite method: 0.000165 Simpson's composite method: 0.000168 Simpson's composite method: 0.000171 Simpson's composite method: 0.000174 Simpson's composite method: 0.000177 Simpson's composite method: 0.000180 Simpson's composite method: 0.000183 Simpson's composite method: 0.000187 Simpson's composite method: 0.000190 Simpson's composite method: 0.000193 Simpson's composite method: 0.000197 Simpson's composite method: 0.000200 Simpson's composite method: 0.000203 Simpson's composite method: 0.000207 Simpson's composite method: 0.000210 Simpson's composite method: 0.000214 Simpson's composite method: 0.000218 Simpson's composite method: 0.000222 Simpson's composite method: 0.000225 Simpson's composite method: 0.000229 Simpson's composite method: 0.000233 Simpson's composite method: 0.000237 Simpson's composite method: 0.000241 Simpson's composite method: 0.000245 Simpson's composite method: 0.000250 Simpson's composite method: 0.000254 Simpson's composite method: 0.000258 Simpson's composite method: 0.000263 Simpson's composite method: 0.000267 Simpson's composite method: 0.000272 Simpson's composite method: 0.000276 Simpson's composite method: 0.000281 Simpson's composite method: 0.000286 Simpson's composite method: 0.000291 Simpson's composite method: 0.000296 Simpson's composite method: 0.000301 Simpson's composite method: 0.000306 Simpson's composite method: 0.000311 Simpson's composite method: 0.000316 Simpson's composite method: 0.000321 Simpson's composite method: 0.000327 Simpson's composite method: 0.000332 Simpson's composite method: 0.000338 Simpson's composite method: 0.000344 Simpson's composite method: 0.000349 Simpson's composite method: 0.000355 Simpson's composite method: 0.000361 Simpson's composite method: 0.000367 Simpson's composite method: 0.000373 Simpson's composite method: 0.000380 Simpson's composite method: 0.000386 Simpson's composite method: 0.000392 Simpson's composite method: 0.000399 Simpson's composite method: 0.000406 Simpson's composite method: 0.000412 Simpson's composite method: 0.000419 Simpson's composite method: 0.000426 Simpson's composite method: 0.000433 Simpson's composite method: 0.000440 Simpson's composite method: 0.000447 Simpson's composite method: 0.000455 Simpson's composite method: 0.000462 Simpson's composite method: 0.000470 Simpson's composite method: 0.000477 Simpson's composite method: 0.000485 Simpson's composite method: 0.000493 Simpson's composite method: 0.000501 Simpson's composite method: 0.000509 Simpson's composite method: 0.000518 Simpson's composite method: 0.000526 Simpson's composite method: 0.000534 Simpson's composite method: 0.000543 Simpson's composite method: 0.000552 Simpson's composite method: 0.000561 Simpson's composite method: 0.000570 Simpson's composite method: 0.000579 Simpson's composite method: 0.000588 Simpson's composite method: 0.000597 Simpson's composite method: 0.000607 Simpson's composite method: 0.000616 Simpson's composite method: 0.000626 Simpson's composite method: 0.000636 Simpson's composite method: 0.000646 Simpson's composite method: 0.000656 Simpson's composite method: 0.000666 Simpson's composite method: 0.000677 Simpson's composite method: 0.000687 Simpson's composite method: 0.000698 Simpson's composite method: 0.000709 Simpson's composite method: 0.000720 Simpson's composite method: 0.000731 Simpson's composite method: 0.000742 Simpson's composite method: 0.000754 Simpson's composite method: 0.000765 Simpson's composite method: 0.000777 Simpson's composite method: 0.000789 Simpson's composite method: 0.000801 Simpson's composite method: 0.000813 Simpson's composite method: 0.000825 Simpson's composite method: 0.000837 Simpson's composite method: 0.000850 Simpson's composite method: 0.000863 Simpson's composite method: 0.000876 Simpson's composite method: 0.000889 Simpson's composite method: 0.000902 Simpson's composite method: 0.000915 Simpson's composite method: 0.000929 Simpson's composite method: 0.000942 Simpson's composite method: 0.000956 Simpson's composite method: 0.000970 Simpson's composite method: 0.000984 Simpson's composite method: 0.000999 Simpson's composite method: 0.001013 Simpson's composite method: 0.001028 Simpson's composite method: 0.001042 Simpson's composite method: 0.001057 Simpson's composite method: 0.001072 Simpson's composite method: 0.001088 Simpson's composite method: 0.001103 Simpson's composite method: 0.001119 Simpson's composite method: 0.001134 Simpson's composite method: 0.001150 Simpson's composite method: 0.001166 Simpson's composite method: 0.001182 Simpson's composite method: 0.001199 Simpson's composite method: 0.001215 Simpson's composite method: 0.001232 Simpson's composite method: 0.001249 Simpson's composite method: 0.001266 Simpson's composite method: 0.001283 Simpson's composite method: 0.001300 Simpson's composite method: 0.001318 Simpson's composite method: 0.001336 Simpson's composite method: 0.001353 Simpson's composite method: 0.001371 Simpson's composite method: 0.001389 Simpson's composite method: 0.001408 Simpson's composite method: 0.001426 Simpson's composite method: 0.001445 Simpson's composite method: 0.001463 Simpson's composite method: 0.001482 Simpson's composite method: 0.001501 Simpson's composite method: 0.001520 Simpson's composite method: 0.001540 Simpson's composite method: 0.001559 Simpson's composite method: 0.001579 Simpson's composite method: 0.001599 Simpson's composite method: 0.001618 Simpson's composite method: 0.001638 Simpson's composite method: 0.001659 Simpson's composite method: 0.001679 Simpson's composite method: 0.001699 Simpson's composite method: 0.001720 Simpson's composite method: 0.001741 Simpson's composite method: 0.001761 Simpson's composite method: 0.001782 Simpson's composite method: 0.001803 Simpson's composite method: 0.001825 Simpson's composite method: 0.001846 Simpson's composite method: 0.001867 Simpson's composite method: 0.001889 Simpson's composite method: 0.001911 Simpson's composite method: 0.001932 Simpson's composite method: 0.001954 Simpson's composite method: 0.001976 Simpson's composite method: 0.001998 Simpson's composite method: 0.002020 Simpson's composite method: 0.002043 Simpson's composite method: 0.002065 Simpson's composite method: 0.002087 Simpson's composite method: 0.002110 Simpson's composite method: 0.002132 Simpson's composite method: 0.002155 Simpson's composite method: 0.002178 Simpson's composite method: 0.002200 Simpson's composite method: 0.002223 Simpson's composite method: 0.002246 Simpson's composite method: 0.002269 Simpson's composite method: 0.002292 Simpson's composite method: 0.002315 Simpson's composite method: 0.002338 Simpson's composite method: 0.002361 Simpson's composite method: 0.002384 Simpson's composite method: 0.002408 Simpson's composite method: 0.002431 Simpson's composite method: 0.002454 Simpson's composite method: 0.002477 Simpson's composite method: 0.002500 Simpson's composite method: 0.002524 Simpson's composite method: 0.002547 Simpson's composite method: 0.002570 Simpson's composite method: 0.002593 Simpson's composite method: 0.002616 Simpson's composite method: 0.002640 Simpson's composite method: 0.002663 Simpson's composite method: 0.002686 Simpson's composite method: 0.002709 Simpson's composite method: 0.002732 Simpson's composite method: 0.002755 Simpson's composite method: 0.002778 Simpson's composite method: 0.002800 Simpson's composite method: 0.002823 Simpson's composite method: 0.002846 Simpson's composite method: 0.002868 Simpson's composite method: 0.002891 Simpson's composite method: 0.002913 Simpson's composite method: 0.002936 Simpson's composite method: 0.002958 Simpson's composite method: 0.002980 Simpson's composite method: 0.003002 Simpson's composite method: 0.003024 Simpson's composite method: 0.003045 Simpson's composite method: 0.003067 Simpson's composite method: 0.003088 Simpson's composite method: 0.003110 Simpson's composite method: 0.003131 Simpson's composite method: 0.003152 Simpson's composite method: 0.003172 Simpson's composite method: 0.003193 Simpson's composite method: 0.003213 Simpson's composite method: 0.003234 Simpson's composite method: 0.003254 Simpson's composite method: 0.003273 Simpson's composite method: 0.003293 Simpson's composite method: 0.003312 Simpson's composite method: 0.003332 Simpson's composite method: 0.003351 Simpson's composite method: 0.003369 Simpson's composite method: 0.003388 Simpson's composite method: 0.003406 Simpson's composite method: 0.003424 Simpson's composite method: 0.003442 Simpson's composite method: 0.003459 Simpson's composite method: 0.003476 Simpson's composite method: 0.003493 Simpson's composite method: 0.003510 Simpson's composite method: 0.003526 Simpson's composite method: 0.003542 Simpson's composite method: 0.003558 Simpson's composite method: 0.003573 Simpson's composite method: 0.003589 Simpson's composite method: 0.003603 Simpson's composite method: 0.003618 Simpson's composite method: 0.003632 Simpson's composite method: 0.003646 Simpson's composite method: 0.003659 Simpson's composite method: 0.003673 Simpson's composite method: 0.003685 Simpson's composite method: 0.003698 Simpson's composite method: 0.003710 Simpson's composite method: 0.003722 Simpson's composite method: 0.003733 Simpson's composite method: 0.003744 Simpson's composite method: 0.003755 Simpson's composite method: 0.003765 Simpson's composite method: 0.003775 Simpson's composite method: 0.003784 Simpson's composite method: 0.003794 Simpson's composite method: 0.003802 Simpson's composite method: 0.003811 Simpson's composite method: 0.003819 Simpson's composite method: 0.003826 Simpson's composite method: 0.003833 Simpson's composite method: 0.003840 Simpson's composite method: 0.003846 Simpson's composite method: 0.003852 Simpson's composite method: 0.003858 Simpson's composite method: 0.003863 Simpson's composite method: 0.003868 Simpson's composite method: 0.003872 Simpson's composite method: 0.003876 Simpson's composite method: 0.003879 Simpson's composite method: 0.003882 Simpson's composite method: 0.003885 Simpson's composite method: 0.003887 Simpson's composite method: 0.003888 Simpson's composite method: 0.003890 Simpson's composite method: 0.003891 Simpson's composite method: 0.003891 Simpson's composite method: 0.003891 Simpson's composite method: 0.003891 Simpson's composite method: 0.003890 Simpson's composite method: 0.003888 Simpson's composite method: 0.003887 Simpson's composite method: 0.003885 Simpson's composite method: 0.003882 Simpson's composite method: 0.003879 Simpson's composite method: 0.003876 Simpson's composite method: 0.003872 Simpson's composite method: 0.003868 Simpson's composite method: 0.003863 Simpson's composite method: 0.003858 Simpson's composite method: 0.003852 Simpson's composite method: 0.003846 Simpson's composite method: 0.003840 Simpson's composite method: 0.003833 Simpson's composite method: 0.003826 Simpson's composite method: 0.003819 Simpson's composite method: 0.003811 Simpson's composite method: 0.003802 Simpson's composite method: 0.003794 Simpson's composite method: 0.003784 Simpson's composite method: 0.003775 Simpson's composite method: 0.003765 Simpson's composite method: 0.003755 Simpson's composite method: 0.003744 Simpson's composite method: 0.003733 Simpson's composite method: 0.003722 Simpson's composite method: 0.003710 Simpson's composite method: 0.003698 Simpson's composite method: 0.003685 Simpson's composite method: 0.003673 Simpson's composite method: 0.003659 Simpson's composite method: 0.003646 Simpson's composite method: 0.003632 Simpson's composite method: 0.003618 Simpson's composite method: 0.003603 Simpson's composite method: 0.003589 Simpson's composite method: 0.003573 Simpson's composite method: 0.003558 Simpson's composite method: 0.003542 Simpson's composite method: 0.003526 Simpson's composite method: 0.003510 Simpson's composite method: 0.003493 Simpson's composite method: 0.003476 Simpson's composite method: 0.003459 Simpson's composite method: 0.003442 Simpson's composite method: 0.003424 Simpson's composite method: 0.003406 Simpson's composite method: 0.003388 Simpson's composite method: 0.003369 Simpson's composite method: 0.003351 Simpson's composite method: 0.003332 Simpson's composite method: 0.003312 Simpson's composite method: 0.003293 Simpson's composite method: 0.003273 Simpson's composite method: 0.003254 Simpson's composite method: 0.003234 Simpson's composite method: 0.003213 Simpson's composite method: 0.003193 Simpson's composite method: 0.003172 Simpson's composite method: 0.003152 Simpson's composite method: 0.003131 Simpson's composite method: 0.003110 Simpson's composite method: 0.003088 Simpson's composite method: 0.003067 Simpson's composite method: 0.003045 Simpson's composite method: 0.003024 Simpson's composite method: 0.003002 Simpson's composite method: 0.002980 Simpson's composite method: 0.002958 Simpson's composite method: 0.002936 Simpson's composite method: 0.002913 Simpson's composite method: 0.002891 Simpson's composite method: 0.002868 Simpson's composite method: 0.002846 Simpson's composite method: 0.002823 Simpson's composite method: 0.002800 Simpson's composite method: 0.002778 Simpson's composite method: 0.002755 Simpson's composite method: 0.002732 Simpson's composite method: 0.002709 Simpson's composite method: 0.002686 Simpson's composite method: 0.002663 Simpson's composite method: 0.002640 Simpson's composite method: 0.002616 Simpson's composite method: 0.002593 Simpson's composite method: 0.002570 Simpson's composite method: 0.002547 Simpson's composite method: 0.002524 Simpson's composite method: 0.002500 Simpson's composite method: 0.002477 Simpson's composite method: 0.002454 Simpson's composite method: 0.002431 Simpson's composite method: 0.002408 Simpson's composite method: 0.002384 Simpson's composite method: 0.002361 Simpson's composite method: 0.002338 Simpson's composite method: 0.002315 Simpson's composite method: 0.002292 Simpson's composite method: 0.002269 Simpson's composite method: 0.002246 Simpson's composite method: 0.002223 Simpson's composite method: 0.002200 Simpson's composite method: 0.002178 Simpson's composite method: 0.002155 Simpson's composite method: 0.002132 Simpson's composite method: 0.002110 Simpson's composite method: 0.002087 Simpson's composite method: 0.002065 Simpson's composite method: 0.002043 Simpson's composite method: 0.002020 Simpson's composite method: 0.001998 Simpson's composite method: 0.001976 Simpson's composite method: 0.001954 Simpson's composite method: 0.001932 Simpson's composite method: 0.001911 Simpson's composite method: 0.001889 Simpson's composite method: 0.001867 Simpson's composite method: 0.001846 Simpson's composite method: 0.001825 Simpson's composite method: 0.001803 Simpson's composite method: 0.001782 Simpson's composite method: 0.001761 Simpson's composite method: 0.001741 Simpson's composite method: 0.001720 Simpson's composite method: 0.001699 Simpson's composite method: 0.001679 Simpson's composite method: 0.001659 Simpson's composite method: 0.001638 Simpson's composite method: 0.001618 Simpson's composite method: 0.001599 Simpson's composite method: 0.001579 Simpson's composite method: 0.001559 Simpson's composite method: 0.001540 Simpson's composite method: 0.001520 Simpson's composite method: 0.001501 Simpson's composite method: 0.001482 Simpson's composite method: 0.001463 Simpson's composite method: 0.001445 Simpson's composite method: 0.001426 Simpson's composite method: 0.001408 Simpson's composite method: 0.001389 Simpson's composite method: 0.001371 Simpson's composite method: 0.001353 Simpson's composite method: 0.001336 Simpson's composite method: 0.001318 Simpson's composite method: 0.001300 Simpson's composite method: 0.001283 Simpson's composite method: 0.001266 Simpson's composite method: 0.001249 Simpson's composite method: 0.001232 Simpson's composite method: 0.001215 Simpson's composite method: 0.001199 Simpson's composite method: 0.001182 Simpson's composite method: 0.001166 Simpson's composite method: 0.001150 Simpson's composite method: 0.001134 Simpson's composite method: 0.001119 Simpson's composite method: 0.001103 Simpson's composite method: 0.001088 Simpson's composite method: 0.001072 Simpson's composite method: 0.001057 Simpson's composite method: 0.001042 Simpson's composite method: 0.001028 Simpson's composite method: 0.001013 Simpson's composite method: 0.000999 Simpson's composite method: 0.000984 Simpson's composite method: 0.000970 Simpson's composite method: 0.000956 Simpson's composite method: 0.000942 Simpson's composite method: 0.000929 Simpson's composite method: 0.000915 Simpson's composite method: 0.000902 Simpson's composite method: 0.000889 Simpson's composite method: 0.000876 Simpson's composite method: 0.000863 Simpson's composite method: 0.000850 Simpson's composite method: 0.000837 Simpson's composite method: 0.000825 Simpson's composite method: 0.000813 Simpson's composite method: 0.000801 Simpson's composite method: 0.000789 Simpson's composite method: 0.000777 Simpson's composite method: 0.000765 Simpson's composite method: 0.000754 Simpson's composite method: 0.000742 Simpson's composite method: 0.000731 Simpson's composite method: 0.000720 Simpson's composite method: 0.000709 Simpson's composite method: 0.000698 Simpson's composite method: 0.000687 Simpson's composite method: 0.000677 Simpson's composite method: 0.000666 Simpson's composite method: 0.000656 Simpson's composite method: 0.000646 Simpson's composite method: 0.000636 Simpson's composite method: 0.000626 Simpson's composite method: 0.000616 Simpson's composite method: 0.000607 Simpson's composite method: 0.000597 Simpson's composite method: 0.000588 Simpson's composite method: 0.000579 Simpson's composite method: 0.000570 Simpson's composite method: 0.000561 Simpson's composite method: 0.000552 Simpson's composite method: 0.000543 Simpson's composite method: 0.000534 Simpson's composite method: 0.000526 Simpson's composite method: 0.000518 Simpson's composite method: 0.000509 Simpson's composite method: 0.000501 Simpson's composite method: 0.000493 Simpson's composite method: 0.000485 Simpson's composite method: 0.000477 Simpson's composite method: 0.000470 Simpson's composite method: 0.000462 Simpson's composite method: 0.000455 Simpson's composite method: 0.000447 Simpson's composite method: 0.000440 Simpson's composite method: 0.000433 Simpson's composite method: 0.000426 Simpson's composite method: 0.000419 Simpson's composite method: 0.000412 Simpson's composite method: 0.000406 Simpson's composite method: 0.000399 Simpson's composite method: 0.000392 Simpson's composite method: 0.000386 Simpson's composite method: 0.000380 Simpson's composite method: 0.000373 Simpson's composite method: 0.000367 Simpson's composite method: 0.000361 Simpson's composite method: 0.000355 Simpson's composite method: 0.000349 Simpson's composite method: 0.000344 Simpson's composite method: 0.000338 Simpson's composite method: 0.000332 Simpson's composite method: 0.000327 Simpson's composite method: 0.000321 Simpson's composite method: 0.000316 Simpson's composite method: 0.000311 Simpson's composite method: 0.000306 Simpson's composite method: 0.000301 Simpson's composite method: 0.000296 Simpson's composite method: 0.000291 Simpson's composite method: 0.000286 Simpson's composite method: 0.000281 Simpson's composite method: 0.000276 Simpson's composite method: 0.000272 Simpson's composite method: 0.000267 Simpson's composite method: 0.000263 Simpson's composite method: 0.000258 Simpson's composite method: 0.000254 Simpson's composite method: 0.000250 Simpson's composite method: 0.000245 Simpson's composite method: 0.000241 Simpson's composite method: 0.000237 Simpson's composite method: 0.000233 Simpson's composite method: 0.000229 Simpson's composite method: 0.000225 Simpson's composite method: 0.000222 Simpson's composite method: 0.000218 Simpson's composite method: 0.000214 Simpson's composite method: 0.000210 Simpson's composite method: 0.000207 Simpson's composite method: 0.000203 Simpson's composite method: 0.000200 Simpson's composite method: 0.000197 Simpson's composite method: 0.000193 Simpson's composite method: 0.000190 Simpson's composite method: 0.000187 Simpson's composite method: 0.000183 Simpson's composite method: 0.000180 Simpson's composite method: 0.000177 Simpson's composite method: 0.000174 Simpson's composite method: 0.000171 Simpson's composite method: 0.000168 Simpson's composite method: 0.000165 Simpson's composite method: 0.000163 Simpson's composite method: 0.000160 Simpson's composite method: 0.000157 Simpson's composite method: 0.000154 Simpson's composite method: 0.000152 Simpson's composite method: 0.000149 Simpson's composite method: 0.000147 Simpson's composite method: 0.000144 Simpson's composite method: 0.000142 Simpson's composite method: 0.000139 Simpson's composite method: 0.000137 Simpson's composite method: 0.000134 Simpson's composite method: 0.000132 Simpson's composite method: 0.000130 Simpson's composite method: 0.000128 Simpson's composite method: 0.000125 Simpson's composite method: 0.000123 Simpson's composite method: 0.000121 Simpson's composite method: 0.000119 Simpson's composite method: 0.000117 Simpson's composite method: 0.000115 Simpson's composite method: 0.000113 Simpson's composite method: 0.000111 Simpson's composite method: 0.000109 Simpson's composite method: 0.000107 Simpson's composite method: 0.000105 Simpson's composite method: 0.000104 Simpson's composite method: 0.000102 Simpson's composite method: 0.000100 Simpson's composite method: 0.000098 Simpson's composite method: 0.000097 Simpson's composite method: 0.000095 Simpson's composite method: 0.000093 Simpson's composite method: 0.000092 Simpson's composite method: 0.000090 Simpson's composite method: 0.000089 Simpson's composite method: 0.000087 Simpson's composite method: 0.000086 Simpson's composite method: 0.000084 Simpson's composite method: 0.000083 Simpson's composite method: 0.000081 Simpson's composite method: 0.000080 Simpson's composite method: 0.000078 Simpson's composite method: 0.000077 Simpson's composite method: 0.000076 Simpson's composite method: 0.000074 Simpson's composite method: 0.000073 Simpson's composite method: 0.000072 Simpson's composite method: 0.000071 Simpson's composite method: 0.000069 Simpson's composite method: 0.000068 Simpson's composite method: 0.000067 Simpson's composite method: 0.000066 Simpson's composite method: 0.000065 Simpson's composite method: 0.000064 Simpson's composite method: 0.000063 Simpson's composite method: 0.000062 Simpson's composite method: 0.000060 Simpson's composite method: 0.000059 Simpson's composite method: 0.000058 Simpson's composite method: 0.000057 Simpson's composite method: 0.000056 Simpson's composite method: 0.000055 Simpson's composite method: 0.000054 Simpson's composite method: 0.000054 Simpson's composite method: 0.000053 Simpson's composite method: 0.000052 Simpson's composite method: 0.000051 Simpson's composite method: 0.000050 Simpson's composite method: 0.000049 Simpson's composite method: 0.000048 Simpson's composite method: 0.000047 Simpson's composite method: 0.000047 Simpson's composite method: 0.000046 Simpson's composite method: 0.000045 Simpson's composite method: 0.000044 Simpson's composite method: 0.000043 Simpson's composite method: 0.000043 Simpson's composite method: 0.000042 Simpson's composite method: 0.000041 Simpson's composite method: 0.000041 Simpson's composite method: 0.000040 Simpson's composite method: 0.000039 Simpson's composite method: 0.000039 Simpson's composite method: 0.000038 Simpson's composite method: 0.000037 Simpson's composite method: 0.000037 Simpson's composite method: 0.000036 Simpson's composite method: 0.000035 Simpson's composite method: 0.000035 Simpson's composite method: 0.000034 Simpson's composite method: 0.000034 Simpson's composite method: 0.000033 Simpson's composite method: 0.000032 Simpson's composite method: 0.000032 Simpson's composite method: 0.000031 Simpson's composite method: 0.000031 Simpson's composite method: 0.000030 Simpson's composite method: 0.000030 Simpson's composite method: 0.000029 Simpson's composite method: 0.000029 Simpson's composite method: 0.000028 Simpson's composite method: 0.000028 Simpson's composite method: 0.000027 Simpson's composite method: 0.000027 Simpson's composite method: 0.000026 Simpson's composite method: 0.000026 Simpson's composite method: 0.000026 Simpson's composite method: 0.000025 Simpson's composite method: 0.000025 Simpson's composite method: 0.000024 Simpson's composite method: 0.000024 Simpson's composite method: 0.000023 Simpson's composite method: 0.000023 Simpson's composite method: 0.000023 Simpson's composite method: 0.000022 Simpson's composite method: 0.000022 Simpson's composite method: 0.000022 Simpson's composite method: 0.000021 Simpson's composite method: 0.000021 Simpson's composite method: 0.000020 Simpson's composite method: 0.000020 Simpson's composite method: 0.000020 Simpson's composite method: 0.000019 Simpson's composite method: 0.000019 Simpson's composite method: 0.000019 Simpson's composite method: 0.000019 Simpson's composite method: 0.000018 Simpson's composite method: 0.000018 Simpson's composite method: 0.000018 Simpson's composite method: 0.000017 Simpson's composite method: 0.000017 Simpson's composite method: 0.000017 Simpson's composite method: 0.000016 Simpson's composite method: 0.000016 Simpson's composite method: 0.000016 Simpson's composite method: 0.000016 Simpson's composite method: 0.000015 Simpson's composite method: 0.000015 Simpson's composite method: 0.000015 Simpson's composite method: 0.000015 Simpson's composite method: 0.000014 Simpson's composite method: 0.000014 Simpson's composite method: 0.000014 Simpson's composite method: 0.000014 Simpson's composite method: 0.000013 Simpson's composite method: 0.000013 Simpson's composite method: 0.000013 Simpson's composite method: 0.000013 Simpson's composite method: 0.000013 Simpson's composite method: 0.000012 Simpson's composite method: 0.000012 Simpson's composite method: 0.000012 Simpson's composite method: 0.000012 Simpson's composite method: 0.000012 Simpson's composite method: 0.000011 Simpson's composite method: 0.000011 Simpson's composite method: 0.000011 Simpson's composite method: 0.000011 Simpson's composite method: 0.000011 Simpson's composite method: 0.000010 Simpson's composite method: 0.000010 Simpson's composite method: 0.000010 Simpson's composite method: 0.000010 Simpson's composite method: 0.000010 Simpson's composite method: 0.000010 Simpson's composite method: 0.000010 Simpson's composite method: 0.000009 Simpson's composite method: 0.000009 Simpson's composite method: 0.000009 Simpson's composite method: 0.000009 Simpson's composite method: 0.000009 Simpson's composite method: 0.000009 Simpson's composite method: 0.000008 Simpson's composite method: 0.000008 Simpson's composite method: 0.000008 Simpson's composite method: 0.000008 Simpson's composite method: 0.000008 Simpson's composite method: 0.000008 Simpson's composite method: 0.000008 Simpson's composite method: 0.000008 Simpson's composite method: 0.000007 Simpson's composite method: 0.000007 Simpson's composite method: 0.000007 Simpson's composite method: 0.000007 Simpson's composite method: 0.000007 Simpson's composite method: 0.000007 Simpson's composite method: 0.000007 Simpson's composite method: 0.000007 Simpson's composite method: 0.000007 Simpson's composite method: 0.000006 Simpson's composite method: 0.000006 Simpson's composite method: 0.000006 Simpson's composite method: 0.000006 Simpson's composite method: 0.000006 Simpson's composite method: 0.000006 Simpson's composite method: 0.000006 Simpson's composite method: 0.000006 Simpson's composite method: 0.000006 Simpson's composite method: 0.000006 Simpson's composite method: 0.000005 Simpson's composite method: 0.000005 Simpson's composite method: 0.000005 Simpson's composite method: 0.000005 Simpson's composite method: 0.000005 Simpson's composite method: 0.000005 Simpson's composite method: 0.000005 Simpson's composite method: 0.000005 Simpson's composite method: 0.000005 Simpson's composite method: 0.000005 Simpson's composite method: 0.000005 Simpson's composite method: 0.000005 Simpson's composite method: 0.000005 Simpson's composite method: 0.000004 Simpson's composite method: 0.000004 Simpson's composite method: 0.000004 Simpson's composite method: 0.000004 Simpson's composite method: 0.000004 Simpson's composite method: 0.000004 Simpson's composite method: 0.000004 Simpson's composite method: 0.000004

fprintf('Exact value: %f\n', t_exact);

Exact value: 1.000000

fprintf('\nNormal distribution integral:\n');

Normal distribution integral:

fprintf('Trapezoid method: %f\n', norm_trap);

Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000002 Trapezoid method: 0.000002 Trapezoid method: 0.000002 Trapezoid method: 0.000002 Trapezoid method: 0.000002 Trapezoid method: 0.000002 Trapezoid method: 0.000002 Trapezoid method: 0.000002 Trapezoid method: 0.000002 Trapezoid method: 0.000002 Trapezoid method: 0.000002 Trapezoid method: 0.000002 Trapezoid method: 0.000002 Trapezoid method: 0.000003 Trapezoid method: 0.000003 Trapezoid method: 0.000003 Trapezoid method: 0.000003 Trapezoid method: 0.000003 Trapezoid method: 0.000003 Trapezoid method: 0.000003 Trapezoid method: 0.000003 Trapezoid method: 0.000003 Trapezoid method: 0.000004 Trapezoid method: 0.000004 Trapezoid method: 0.000004 Trapezoid method: 0.000004 Trapezoid method: 0.000004 Trapezoid method: 0.000004 Trapezoid method: 0.000004 Trapezoid method: 0.000005 Trapezoid method: 0.000005 Trapezoid method: 0.000005 Trapezoid method: 0.000005 Trapezoid method: 0.000005 Trapezoid method: 0.000006 Trapezoid method: 0.000006 Trapezoid method: 0.000006 Trapezoid method: 0.000006 Trapezoid method: 0.000006 Trapezoid method: 0.000007 Trapezoid method: 0.000007 Trapezoid method: 0.000007 Trapezoid method: 0.000007 Trapezoid method: 0.000008 Trapezoid method: 0.000008 Trapezoid method: 0.000008 Trapezoid method: 0.000009 Trapezoid method: 0.000009 Trapezoid method: 0.000009 Trapezoid method: 0.000010 Trapezoid method: 0.000010 Trapezoid method: 0.000010 Trapezoid method: 0.000011 Trapezoid method: 0.000011 Trapezoid method: 0.000011 Trapezoid method: 0.000012 Trapezoid method: 0.000012 Trapezoid method: 0.000013 Trapezoid method: 0.000013 Trapezoid method: 0.000013 Trapezoid method: 0.000014 Trapezoid method: 0.000014 Trapezoid method: 0.000015 Trapezoid method: 0.000015 Trapezoid method: 0.000016 Trapezoid method: 0.000016 Trapezoid method: 0.000017 Trapezoid method: 0.000018 Trapezoid method: 0.000018 Trapezoid method: 0.000019 Trapezoid method: 0.000019 Trapezoid method: 0.000020 Trapezoid method: 0.000021 Trapezoid method: 0.000021 Trapezoid method: 0.000022 Trapezoid method: 0.000023 Trapezoid method: 0.000023 Trapezoid method: 0.000024 Trapezoid method: 0.000025 Trapezoid method: 0.000026 Trapezoid method: 0.000027 Trapezoid method: 0.000028 Trapezoid method: 0.000028 Trapezoid method: 0.000029 Trapezoid method: 0.000030 Trapezoid method: 0.000031 Trapezoid method: 0.000032 Trapezoid method: 0.000033 Trapezoid method: 0.000034 Trapezoid method: 0.000035 Trapezoid method: 0.000036 Trapezoid method: 0.000038 Trapezoid method: 0.000039 Trapezoid method: 0.000040 Trapezoid method: 0.000041 Trapezoid method: 0.000042 Trapezoid method: 0.000044 Trapezoid method: 0.000045 Trapezoid method: 0.000046 Trapezoid method: 0.000048 Trapezoid method: 0.000049 Trapezoid method: 0.000051 Trapezoid method: 0.000052 Trapezoid method: 0.000054 Trapezoid method: 0.000055 Trapezoid method: 0.000057 Trapezoid method: 0.000059 Trapezoid method: 0.000060 Trapezoid method: 0.000062 Trapezoid method: 0.000064 Trapezoid method: 0.000066 Trapezoid method: 0.000068 Trapezoid method: 0.000070 Trapezoid method: 0.000072 Trapezoid method: 0.000074 Trapezoid method: 0.000076 Trapezoid method: 0.000078 Trapezoid method: 0.000080 Trapezoid method: 0.000083 Trapezoid method: 0.000085 Trapezoid method: 0.000087 Trapezoid method: 0.000090 Trapezoid method: 0.000092 Trapezoid method: 0.000095 Trapezoid method: 0.000097 Trapezoid method: 0.000100 Trapezoid method: 0.000103 Trapezoid method: 0.000106 Trapezoid method: 0.000109 Trapezoid method: 0.000111 Trapezoid method: 0.000114 Trapezoid method: 0.000118 Trapezoid method: 0.000121 Trapezoid method: 0.000124 Trapezoid method: 0.000127 Trapezoid method: 0.000131 Trapezoid method: 0.000134 Trapezoid method: 0.000138 Trapezoid method: 0.000141 Trapezoid method: 0.000145 Trapezoid method: 0.000149 Trapezoid method: 0.000153 Trapezoid method: 0.000156 Trapezoid method: 0.000161 Trapezoid method: 0.000165 Trapezoid method: 0.000169 Trapezoid method: 0.000173 Trapezoid method: 0.000177 Trapezoid method: 0.000182 Trapezoid method: 0.000187 Trapezoid method: 0.000191 Trapezoid method: 0.000196 Trapezoid method: 0.000201 Trapezoid method: 0.000206 Trapezoid method: 0.000211 Trapezoid method: 0.000216 Trapezoid method: 0.000221 Trapezoid method: 0.000227 Trapezoid method: 0.000232 Trapezoid method: 0.000238 Trapezoid method: 0.000243 Trapezoid method: 0.000249 Trapezoid method: 0.000255 Trapezoid method: 0.000261 Trapezoid method: 0.000267 Trapezoid method: 0.000274 Trapezoid method: 0.000280 Trapezoid method: 0.000287 Trapezoid method: 0.000293 Trapezoid method: 0.000300 Trapezoid method: 0.000307 Trapezoid method: 0.000314 Trapezoid method: 0.000321 Trapezoid method: 0.000328 Trapezoid method: 0.000336 Trapezoid method: 0.000343 Trapezoid method: 0.000351 Trapezoid method: 0.000359 Trapezoid method: 0.000367 Trapezoid method: 0.000375 Trapezoid method: 0.000383 Trapezoid method: 0.000391 Trapezoid method: 0.000400 Trapezoid method: 0.000408 Trapezoid method: 0.000417 Trapezoid method: 0.000426 Trapezoid method: 0.000435 Trapezoid method: 0.000444 Trapezoid method: 0.000454 Trapezoid method: 0.000463 Trapezoid method: 0.000473 Trapezoid method: 0.000483 Trapezoid method: 0.000493 Trapezoid method: 0.000503 Trapezoid method: 0.000513 Trapezoid method: 0.000524 Trapezoid method: 0.000535 Trapezoid method: 0.000545 Trapezoid method: 0.000556 Trapezoid method: 0.000567 Trapezoid method: 0.000579 Trapezoid method: 0.000590 Trapezoid method: 0.000602 Trapezoid method: 0.000614 Trapezoid method: 0.000626 Trapezoid method: 0.000638 Trapezoid method: 0.000650 Trapezoid method: 0.000662 Trapezoid method: 0.000675 Trapezoid method: 0.000688 Trapezoid method: 0.000701 Trapezoid method: 0.000714 Trapezoid method: 0.000727 Trapezoid method: 0.000741 Trapezoid method: 0.000755 Trapezoid method: 0.000768 Trapezoid method: 0.000782 Trapezoid method: 0.000797 Trapezoid method: 0.000811 Trapezoid method: 0.000826 Trapezoid method: 0.000840 Trapezoid method: 0.000855 Trapezoid method: 0.000870 Trapezoid method: 0.000886 Trapezoid method: 0.000901 Trapezoid method: 0.000917 Trapezoid method: 0.000933 Trapezoid method: 0.000949 Trapezoid method: 0.000965 Trapezoid method: 0.000981 Trapezoid method: 0.000998 Trapezoid method: 0.001014 Trapezoid method: 0.001031 Trapezoid method: 0.001048 Trapezoid method: 0.001065 Trapezoid method: 0.001083 Trapezoid method: 0.001100 Trapezoid method: 0.001118 Trapezoid method: 0.001136 Trapezoid method: 0.001154 Trapezoid method: 0.001172 Trapezoid method: 0.001191 Trapezoid method: 0.001209 Trapezoid method: 0.001228 Trapezoid method: 0.001247 Trapezoid method: 0.001266 Trapezoid method: 0.001286 Trapezoid method: 0.001305 Trapezoid method: 0.001325 Trapezoid method: 0.001344 Trapezoid method: 0.001364 Trapezoid method: 0.001384 Trapezoid method: 0.001404 Trapezoid method: 0.001425 Trapezoid method: 0.001445 Trapezoid method: 0.001466 Trapezoid method: 0.001487 Trapezoid method: 0.001508 Trapezoid method: 0.001529 Trapezoid method: 0.001550 Trapezoid method: 0.001572 Trapezoid method: 0.001593 Trapezoid method: 0.001615 Trapezoid method: 0.001636 Trapezoid method: 0.001658 Trapezoid method: 0.001680 Trapezoid method: 0.001703 Trapezoid method: 0.001725 Trapezoid method: 0.001747 Trapezoid method: 0.001770 Trapezoid method: 0.001792 Trapezoid method: 0.001815 Trapezoid method: 0.001838 Trapezoid method: 0.001861 Trapezoid method: 0.001884 Trapezoid method: 0.001907 Trapezoid method: 0.001930 Trapezoid method: 0.001954 Trapezoid method: 0.001977 Trapezoid method: 0.002000 Trapezoid method: 0.002024 Trapezoid method: 0.002048 Trapezoid method: 0.002071 Trapezoid method: 0.002095 Trapezoid method: 0.002119 Trapezoid method: 0.002143 Trapezoid method: 0.002167 Trapezoid method: 0.002191 Trapezoid method: 0.002215 Trapezoid method: 0.002239 Trapezoid method: 0.002263 Trapezoid method: 0.002287 Trapezoid method: 0.002311 Trapezoid method: 0.002335 Trapezoid method: 0.002359 Trapezoid method: 0.002383 Trapezoid method: 0.002408 Trapezoid method: 0.002432 Trapezoid method: 0.002456 Trapezoid method: 0.002480 Trapezoid method: 0.002504 Trapezoid method: 0.002529 Trapezoid method: 0.002553 Trapezoid method: 0.002577 Trapezoid method: 0.002601 Trapezoid method: 0.002625 Trapezoid method: 0.002649 Trapezoid method: 0.002673 Trapezoid method: 0.002697 Trapezoid method: 0.002721 Trapezoid method: 0.002744 Trapezoid method: 0.002768 Trapezoid method: 0.002792 Trapezoid method: 0.002815 Trapezoid method: 0.002839 Trapezoid method: 0.002862 Trapezoid method: 0.002885 Trapezoid method: 0.002908 Trapezoid method: 0.002932 Trapezoid method: 0.002954 Trapezoid method: 0.002977 Trapezoid method: 0.003000 Trapezoid method: 0.003023 Trapezoid method: 0.003045 Trapezoid method: 0.003067 Trapezoid method: 0.003090 Trapezoid method: 0.003112 Trapezoid method: 0.003133 Trapezoid method: 0.003155 Trapezoid method: 0.003177 Trapezoid method: 0.003198 Trapezoid method: 0.003219 Trapezoid method: 0.003240 Trapezoid method: 0.003261 Trapezoid method: 0.003282 Trapezoid method: 0.003302 Trapezoid method: 0.003322 Trapezoid method: 0.003342 Trapezoid method: 0.003362 Trapezoid method: 0.003382 Trapezoid method: 0.003401 Trapezoid method: 0.003420 Trapezoid method: 0.003439 Trapezoid method: 0.003457 Trapezoid method: 0.003476 Trapezoid method: 0.003494 Trapezoid method: 0.003512 Trapezoid method: 0.003529 Trapezoid method: 0.003547 Trapezoid method: 0.003564 Trapezoid method: 0.003581 Trapezoid method: 0.003597 Trapezoid method: 0.003613 Trapezoid method: 0.003629 Trapezoid method: 0.003645 Trapezoid method: 0.003660 Trapezoid method: 0.003675 Trapezoid method: 0.003690 Trapezoid method: 0.003704 Trapezoid method: 0.003719 Trapezoid method: 0.003732 Trapezoid method: 0.003746 Trapezoid method: 0.003759 Trapezoid method: 0.003772 Trapezoid method: 0.003784 Trapezoid method: 0.003796 Trapezoid method: 0.003808 Trapezoid method: 0.003820 Trapezoid method: 0.003831 Trapezoid method: 0.003841 Trapezoid method: 0.003852 Trapezoid method: 0.003862 Trapezoid method: 0.003871 Trapezoid method: 0.003881 Trapezoid method: 0.003890 Trapezoid method: 0.003898 Trapezoid method: 0.003906 Trapezoid method: 0.003914 Trapezoid method: 0.003922 Trapezoid method: 0.003929 Trapezoid method: 0.003935 Trapezoid method: 0.003942 Trapezoid method: 0.003948 Trapezoid method: 0.003953 Trapezoid method: 0.003958 Trapezoid method: 0.003963 Trapezoid method: 0.003967 Trapezoid method: 0.003971 Trapezoid method: 0.003975 Trapezoid method: 0.003978 Trapezoid method: 0.003981 Trapezoid method: 0.003983 Trapezoid method: 0.003985 Trapezoid method: 0.003987 Trapezoid method: 0.003988 Trapezoid method: 0.003989 Trapezoid method: 0.003989 Trapezoid method: 0.003989 Trapezoid method: 0.003989 Trapezoid method: 0.003988 Trapezoid method: 0.003987 Trapezoid method: 0.003985 Trapezoid method: 0.003983 Trapezoid method: 0.003981 Trapezoid method: 0.003978 Trapezoid method: 0.003975 Trapezoid method: 0.003971 Trapezoid method: 0.003967 Trapezoid method: 0.003963 Trapezoid method: 0.003958 Trapezoid method: 0.003953 Trapezoid method: 0.003948 Trapezoid method: 0.003942 Trapezoid method: 0.003935 Trapezoid method: 0.003929 Trapezoid method: 0.003922 Trapezoid method: 0.003914 Trapezoid method: 0.003906 Trapezoid method: 0.003898 Trapezoid method: 0.003890 Trapezoid method: 0.003881 Trapezoid method: 0.003871 Trapezoid method: 0.003862 Trapezoid method: 0.003852 Trapezoid method: 0.003841 Trapezoid method: 0.003831 Trapezoid method: 0.003820 Trapezoid method: 0.003808 Trapezoid method: 0.003796 Trapezoid method: 0.003784 Trapezoid method: 0.003772 Trapezoid method: 0.003759 Trapezoid method: 0.003746 Trapezoid method: 0.003732 Trapezoid method: 0.003719 Trapezoid method: 0.003704 Trapezoid method: 0.003690 Trapezoid method: 0.003675 Trapezoid method: 0.003660 Trapezoid method: 0.003645 Trapezoid method: 0.003629 Trapezoid method: 0.003613 Trapezoid method: 0.003597 Trapezoid method: 0.003581 Trapezoid method: 0.003564 Trapezoid method: 0.003547 Trapezoid method: 0.003529 Trapezoid method: 0.003512 Trapezoid method: 0.003494 Trapezoid method: 0.003476 Trapezoid method: 0.003457 Trapezoid method: 0.003439 Trapezoid method: 0.003420 Trapezoid method: 0.003401 Trapezoid method: 0.003382 Trapezoid method: 0.003362 Trapezoid method: 0.003342 Trapezoid method: 0.003322 Trapezoid method: 0.003302 Trapezoid method: 0.003282 Trapezoid method: 0.003261 Trapezoid method: 0.003240 Trapezoid method: 0.003219 Trapezoid method: 0.003198 Trapezoid method: 0.003177 Trapezoid method: 0.003155 Trapezoid method: 0.003133 Trapezoid method: 0.003112 Trapezoid method: 0.003090 Trapezoid method: 0.003067 Trapezoid method: 0.003045 Trapezoid method: 0.003023 Trapezoid method: 0.003000 Trapezoid method: 0.002977 Trapezoid method: 0.002954 Trapezoid method: 0.002932 Trapezoid method: 0.002908 Trapezoid method: 0.002885 Trapezoid method: 0.002862 Trapezoid method: 0.002839 Trapezoid method: 0.002815 Trapezoid method: 0.002792 Trapezoid method: 0.002768 Trapezoid method: 0.002744 Trapezoid method: 0.002721 Trapezoid method: 0.002697 Trapezoid method: 0.002673 Trapezoid method: 0.002649 Trapezoid method: 0.002625 Trapezoid method: 0.002601 Trapezoid method: 0.002577 Trapezoid method: 0.002553 Trapezoid method: 0.002529 Trapezoid method: 0.002504 Trapezoid method: 0.002480 Trapezoid method: 0.002456 Trapezoid method: 0.002432 Trapezoid method: 0.002408 Trapezoid method: 0.002383 Trapezoid method: 0.002359 Trapezoid method: 0.002335 Trapezoid method: 0.002311 Trapezoid method: 0.002287 Trapezoid method: 0.002263 Trapezoid method: 0.002239 Trapezoid method: 0.002215 Trapezoid method: 0.002191 Trapezoid method: 0.002167 Trapezoid method: 0.002143 Trapezoid method: 0.002119 Trapezoid method: 0.002095 Trapezoid method: 0.002071 Trapezoid method: 0.002048 Trapezoid method: 0.002024 Trapezoid method: 0.002000 Trapezoid method: 0.001977 Trapezoid method: 0.001954 Trapezoid method: 0.001930 Trapezoid method: 0.001907 Trapezoid method: 0.001884 Trapezoid method: 0.001861 Trapezoid method: 0.001838 Trapezoid method: 0.001815 Trapezoid method: 0.001792 Trapezoid method: 0.001770 Trapezoid method: 0.001747 Trapezoid method: 0.001725 Trapezoid method: 0.001703 Trapezoid method: 0.001680 Trapezoid method: 0.001658 Trapezoid method: 0.001636 Trapezoid method: 0.001615 Trapezoid method: 0.001593 Trapezoid method: 0.001572 Trapezoid method: 0.001550 Trapezoid method: 0.001529 Trapezoid method: 0.001508 Trapezoid method: 0.001487 Trapezoid method: 0.001466 Trapezoid method: 0.001445 Trapezoid method: 0.001425 Trapezoid method: 0.001404 Trapezoid method: 0.001384 Trapezoid method: 0.001364 Trapezoid method: 0.001344 Trapezoid method: 0.001325 Trapezoid method: 0.001305 Trapezoid method: 0.001286 Trapezoid method: 0.001266 Trapezoid method: 0.001247 Trapezoid method: 0.001228 Trapezoid method: 0.001209 Trapezoid method: 0.001191 Trapezoid method: 0.001172 Trapezoid method: 0.001154 Trapezoid method: 0.001136 Trapezoid method: 0.001118 Trapezoid method: 0.001100 Trapezoid method: 0.001083 Trapezoid method: 0.001065 Trapezoid method: 0.001048 Trapezoid method: 0.001031 Trapezoid method: 0.001014 Trapezoid method: 0.000998 Trapezoid method: 0.000981 Trapezoid method: 0.000965 Trapezoid method: 0.000949 Trapezoid method: 0.000933 Trapezoid method: 0.000917 Trapezoid method: 0.000901 Trapezoid method: 0.000886 Trapezoid method: 0.000870 Trapezoid method: 0.000855 Trapezoid method: 0.000840 Trapezoid method: 0.000826 Trapezoid method: 0.000811 Trapezoid method: 0.000797 Trapezoid method: 0.000782 Trapezoid method: 0.000768 Trapezoid method: 0.000755 Trapezoid method: 0.000741 Trapezoid method: 0.000727 Trapezoid method: 0.000714 Trapezoid method: 0.000701 Trapezoid method: 0.000688 Trapezoid method: 0.000675 Trapezoid method: 0.000662 Trapezoid method: 0.000650 Trapezoid method: 0.000638 Trapezoid method: 0.000626 Trapezoid method: 0.000614 Trapezoid method: 0.000602 Trapezoid method: 0.000590 Trapezoid method: 0.000579 Trapezoid method: 0.000567 Trapezoid method: 0.000556 Trapezoid method: 0.000545 Trapezoid method: 0.000535 Trapezoid method: 0.000524 Trapezoid method: 0.000513 Trapezoid method: 0.000503 Trapezoid method: 0.000493 Trapezoid method: 0.000483 Trapezoid method: 0.000473 Trapezoid method: 0.000463 Trapezoid method: 0.000454 Trapezoid method: 0.000444 Trapezoid method: 0.000435 Trapezoid method: 0.000426 Trapezoid method: 0.000417 Trapezoid method: 0.000408 Trapezoid method: 0.000400 Trapezoid method: 0.000391 Trapezoid method: 0.000383 Trapezoid method: 0.000375 Trapezoid method: 0.000367 Trapezoid method: 0.000359 Trapezoid method: 0.000351 Trapezoid method: 0.000343 Trapezoid method: 0.000336 Trapezoid method: 0.000328 Trapezoid method: 0.000321 Trapezoid method: 0.000314 Trapezoid method: 0.000307 Trapezoid method: 0.000300 Trapezoid method: 0.000293 Trapezoid method: 0.000287 Trapezoid method: 0.000280 Trapezoid method: 0.000274 Trapezoid method: 0.000267 Trapezoid method: 0.000261 Trapezoid method: 0.000255 Trapezoid method: 0.000249 Trapezoid method: 0.000243 Trapezoid method: 0.000238 Trapezoid method: 0.000232 Trapezoid method: 0.000227 Trapezoid method: 0.000221 Trapezoid method: 0.000216 Trapezoid method: 0.000211 Trapezoid method: 0.000206 Trapezoid method: 0.000201 Trapezoid method: 0.000196 Trapezoid method: 0.000191 Trapezoid method: 0.000187 Trapezoid method: 0.000182 Trapezoid method: 0.000177 Trapezoid method: 0.000173 Trapezoid method: 0.000169 Trapezoid method: 0.000165 Trapezoid method: 0.000161 Trapezoid method: 0.000156 Trapezoid method: 0.000153 Trapezoid method: 0.000149 Trapezoid method: 0.000145 Trapezoid method: 0.000141 Trapezoid method: 0.000138 Trapezoid method: 0.000134 Trapezoid method: 0.000131 Trapezoid method: 0.000127 Trapezoid method: 0.000124 Trapezoid method: 0.000121 Trapezoid method: 0.000118 Trapezoid method: 0.000114 Trapezoid method: 0.000111 Trapezoid method: 0.000109 Trapezoid method: 0.000106 Trapezoid method: 0.000103 Trapezoid method: 0.000100 Trapezoid method: 0.000097 Trapezoid method: 0.000095 Trapezoid method: 0.000092 Trapezoid method: 0.000090 Trapezoid method: 0.000087 Trapezoid method: 0.000085 Trapezoid method: 0.000083 Trapezoid method: 0.000080 Trapezoid method: 0.000078 Trapezoid method: 0.000076 Trapezoid method: 0.000074 Trapezoid method: 0.000072 Trapezoid method: 0.000070 Trapezoid method: 0.000068 Trapezoid method: 0.000066 Trapezoid method: 0.000064 Trapezoid method: 0.000062 Trapezoid method: 0.000060 Trapezoid method: 0.000059 Trapezoid method: 0.000057 Trapezoid method: 0.000055 Trapezoid method: 0.000054 Trapezoid method: 0.000052 Trapezoid method: 0.000051 Trapezoid method: 0.000049 Trapezoid method: 0.000048 Trapezoid method: 0.000046 Trapezoid method: 0.000045 Trapezoid method: 0.000044 Trapezoid method: 0.000042 Trapezoid method: 0.000041 Trapezoid method: 0.000040 Trapezoid method: 0.000039 Trapezoid method: 0.000038 Trapezoid method: 0.000036 Trapezoid method: 0.000035 Trapezoid method: 0.000034 Trapezoid method: 0.000033 Trapezoid method: 0.000032 Trapezoid method: 0.000031 Trapezoid method: 0.000030 Trapezoid method: 0.000029 Trapezoid method: 0.000028 Trapezoid method: 0.000028 Trapezoid method: 0.000027 Trapezoid method: 0.000026 Trapezoid method: 0.000025 Trapezoid method: 0.000024 Trapezoid method: 0.000023 Trapezoid method: 0.000023 Trapezoid method: 0.000022 Trapezoid method: 0.000021 Trapezoid method: 0.000021 Trapezoid method: 0.000020 Trapezoid method: 0.000019 Trapezoid method: 0.000019 Trapezoid method: 0.000018 Trapezoid method: 0.000018 Trapezoid method: 0.000017 Trapezoid method: 0.000016 Trapezoid method: 0.000016 Trapezoid method: 0.000015 Trapezoid method: 0.000015 Trapezoid method: 0.000014 Trapezoid method: 0.000014 Trapezoid method: 0.000013 Trapezoid method: 0.000013 Trapezoid method: 0.000013 Trapezoid method: 0.000012 Trapezoid method: 0.000012 Trapezoid method: 0.000011 Trapezoid method: 0.000011 Trapezoid method: 0.000011 Trapezoid method: 0.000010 Trapezoid method: 0.000010 Trapezoid method: 0.000010 Trapezoid method: 0.000009 Trapezoid method: 0.000009 Trapezoid method: 0.000009 Trapezoid method: 0.000008 Trapezoid method: 0.000008 Trapezoid method: 0.000008 Trapezoid method: 0.000007 Trapezoid method: 0.000007 Trapezoid method: 0.000007 Trapezoid method: 0.000007 Trapezoid method: 0.000006 Trapezoid method: 0.000006 Trapezoid method: 0.000006 Trapezoid method: 0.000006 Trapezoid method: 0.000006 Trapezoid method: 0.000005 Trapezoid method: 0.000005 Trapezoid method: 0.000005 Trapezoid method: 0.000005 Trapezoid method: 0.000005 Trapezoid method: 0.000004 Trapezoid method: 0.000004 Trapezoid method: 0.000004 Trapezoid method: 0.000004 Trapezoid method: 0.000004 Trapezoid method: 0.000004 Trapezoid method: 0.000004 Trapezoid method: 0.000003 Trapezoid method: 0.000003 Trapezoid method: 0.000003 Trapezoid method: 0.000003 Trapezoid method: 0.000003 Trapezoid method: 0.000003 Trapezoid method: 0.000003 Trapezoid method: 0.000003 Trapezoid method: 0.000003 Trapezoid method: 0.000002 Trapezoid method: 0.000002 Trapezoid method: 0.000002 Trapezoid method: 0.000002 Trapezoid method: 0.000002 Trapezoid method: 0.000002 Trapezoid method: 0.000002 Trapezoid method: 0.000002 Trapezoid method: 0.000002 Trapezoid method: 0.000002 Trapezoid method: 0.000002 Trapezoid method: 0.000002 Trapezoid method: 0.000002 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000001 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000 Trapezoid method: 0.000000

fprintf('Simpson''s composite method: %f\n', norm_simp);

Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000002 Simpson's composite method: 0.000002 Simpson's composite method: 0.000002 Simpson's composite method: 0.000002 Simpson's composite method: 0.000002 Simpson's composite method: 0.000002 Simpson's composite method: 0.000002 Simpson's composite method: 0.000002 Simpson's composite method: 0.000002 Simpson's composite method: 0.000002 Simpson's composite method: 0.000002 Simpson's composite method: 0.000002 Simpson's composite method: 0.000002 Simpson's composite method: 0.000003 Simpson's composite method: 0.000003 Simpson's composite method: 0.000003 Simpson's composite method: 0.000003 Simpson's composite method: 0.000003 Simpson's composite method: 0.000003 Simpson's composite method: 0.000003 Simpson's composite method: 0.000003 Simpson's composite method: 0.000003 Simpson's composite method: 0.000004 Simpson's composite method: 0.000004 Simpson's composite method: 0.000004 Simpson's composite method: 0.000004 Simpson's composite method: 0.000004 Simpson's composite method: 0.000004 Simpson's composite method: 0.000004 Simpson's composite method: 0.000005 Simpson's composite method: 0.000005 Simpson's composite method: 0.000005 Simpson's composite method: 0.000005 Simpson's composite method: 0.000005 Simpson's composite method: 0.000006 Simpson's composite method: 0.000006 Simpson's composite method: 0.000006 Simpson's composite method: 0.000006 Simpson's composite method: 0.000006 Simpson's composite method: 0.000007 Simpson's composite method: 0.000007 Simpson's composite method: 0.000007 Simpson's composite method: 0.000007 Simpson's composite method: 0.000008 Simpson's composite method: 0.000008 Simpson's composite method: 0.000008 Simpson's composite method: 0.000009 Simpson's composite method: 0.000009 Simpson's composite method: 0.000009 Simpson's composite method: 0.000010 Simpson's composite method: 0.000010 Simpson's composite method: 0.000010 Simpson's composite method: 0.000011 Simpson's composite method: 0.000011 Simpson's composite method: 0.000011 Simpson's composite method: 0.000012 Simpson's composite method: 0.000012 Simpson's composite method: 0.000013 Simpson's composite method: 0.000013 Simpson's composite method: 0.000013 Simpson's composite method: 0.000014 Simpson's composite method: 0.000014 Simpson's composite method: 0.000015 Simpson's composite method: 0.000015 Simpson's composite method: 0.000016 Simpson's composite method: 0.000016 Simpson's composite method: 0.000017 Simpson's composite method: 0.000018 Simpson's composite method: 0.000018 Simpson's composite method: 0.000019 Simpson's composite method: 0.000019 Simpson's composite method: 0.000020 Simpson's composite method: 0.000021 Simpson's composite method: 0.000021 Simpson's composite method: 0.000022 Simpson's composite method: 0.000023 Simpson's composite method: 0.000023 Simpson's composite method: 0.000024 Simpson's composite method: 0.000025 Simpson's composite method: 0.000026 Simpson's composite method: 0.000027 Simpson's composite method: 0.000028 Simpson's composite method: 0.000028 Simpson's composite method: 0.000029 Simpson's composite method: 0.000030 Simpson's composite method: 0.000031 Simpson's composite method: 0.000032 Simpson's composite method: 0.000033 Simpson's composite method: 0.000034 Simpson's composite method: 0.000035 Simpson's composite method: 0.000036 Simpson's composite method: 0.000038 Simpson's composite method: 0.000039 Simpson's composite method: 0.000040 Simpson's composite method: 0.000041 Simpson's composite method: 0.000042 Simpson's composite method: 0.000044 Simpson's composite method: 0.000045 Simpson's composite method: 0.000046 Simpson's composite method: 0.000048 Simpson's composite method: 0.000049 Simpson's composite method: 0.000051 Simpson's composite method: 0.000052 Simpson's composite method: 0.000054 Simpson's composite method: 0.000055 Simpson's composite method: 0.000057 Simpson's composite method: 0.000059 Simpson's composite method: 0.000060 Simpson's composite method: 0.000062 Simpson's composite method: 0.000064 Simpson's composite method: 0.000066 Simpson's composite method: 0.000068 Simpson's composite method: 0.000070 Simpson's composite method: 0.000072 Simpson's composite method: 0.000074 Simpson's composite method: 0.000076 Simpson's composite method: 0.000078 Simpson's composite method: 0.000080 Simpson's composite method: 0.000083 Simpson's composite method: 0.000085 Simpson's composite method: 0.000087 Simpson's composite method: 0.000090 Simpson's composite method: 0.000092 Simpson's composite method: 0.000095 Simpson's composite method: 0.000097 Simpson's composite method: 0.000100 Simpson's composite method: 0.000103 Simpson's composite method: 0.000106 Simpson's composite method: 0.000109 Simpson's composite method: 0.000111 Simpson's composite method: 0.000114 Simpson's composite method: 0.000118 Simpson's composite method: 0.000121 Simpson's composite method: 0.000124 Simpson's composite method: 0.000127 Simpson's composite method: 0.000131 Simpson's composite method: 0.000134 Simpson's composite method: 0.000138 Simpson's composite method: 0.000141 Simpson's composite method: 0.000145 Simpson's composite method: 0.000149 Simpson's composite method: 0.000153 Simpson's composite method: 0.000156 Simpson's composite method: 0.000161 Simpson's composite method: 0.000165 Simpson's composite method: 0.000169 Simpson's composite method: 0.000173 Simpson's composite method: 0.000177 Simpson's composite method: 0.000182 Simpson's composite method: 0.000187 Simpson's composite method: 0.000191 Simpson's composite method: 0.000196 Simpson's composite method: 0.000201 Simpson's composite method: 0.000206 Simpson's composite method: 0.000211 Simpson's composite method: 0.000216 Simpson's composite method: 0.000221 Simpson's composite method: 0.000227 Simpson's composite method: 0.000232 Simpson's composite method: 0.000238 Simpson's composite method: 0.000243 Simpson's composite method: 0.000249 Simpson's composite method: 0.000255 Simpson's composite method: 0.000261 Simpson's composite method: 0.000267 Simpson's composite method: 0.000274 Simpson's composite method: 0.000280 Simpson's composite method: 0.000287 Simpson's composite method: 0.000293 Simpson's composite method: 0.000300 Simpson's composite method: 0.000307 Simpson's composite method: 0.000314 Simpson's composite method: 0.000321 Simpson's composite method: 0.000328 Simpson's composite method: 0.000336 Simpson's composite method: 0.000343 Simpson's composite method: 0.000351 Simpson's composite method: 0.000359 Simpson's composite method: 0.000367 Simpson's composite method: 0.000375 Simpson's composite method: 0.000383 Simpson's composite method: 0.000391 Simpson's composite method: 0.000400 Simpson's composite method: 0.000408 Simpson's composite method: 0.000417 Simpson's composite method: 0.000426 Simpson's composite method: 0.000435 Simpson's composite method: 0.000444 Simpson's composite method: 0.000454 Simpson's composite method: 0.000463 Simpson's composite method: 0.000473 Simpson's composite method: 0.000483 Simpson's composite method: 0.000493 Simpson's composite method: 0.000503 Simpson's composite method: 0.000513 Simpson's composite method: 0.000524 Simpson's composite method: 0.000535 Simpson's composite method: 0.000545 Simpson's composite method: 0.000556 Simpson's composite method: 0.000567 Simpson's composite method: 0.000579 Simpson's composite method: 0.000590 Simpson's composite method: 0.000602 Simpson's composite method: 0.000614 Simpson's composite method: 0.000626 Simpson's composite method: 0.000638 Simpson's composite method: 0.000650 Simpson's composite method: 0.000662 Simpson's composite method: 0.000675 Simpson's composite method: 0.000688 Simpson's composite method: 0.000701 Simpson's composite method: 0.000714 Simpson's composite method: 0.000727 Simpson's composite method: 0.000741 Simpson's composite method: 0.000755 Simpson's composite method: 0.000768 Simpson's composite method: 0.000782 Simpson's composite method: 0.000797 Simpson's composite method: 0.000811 Simpson's composite method: 0.000826 Simpson's composite method: 0.000840 Simpson's composite method: 0.000855 Simpson's composite method: 0.000870 Simpson's composite method: 0.000886 Simpson's composite method: 0.000901 Simpson's composite method: 0.000917 Simpson's composite method: 0.000933 Simpson's composite method: 0.000949 Simpson's composite method: 0.000965 Simpson's composite method: 0.000981 Simpson's composite method: 0.000998 Simpson's composite method: 0.001014 Simpson's composite method: 0.001031 Simpson's composite method: 0.001048 Simpson's composite method: 0.001065 Simpson's composite method: 0.001083 Simpson's composite method: 0.001100 Simpson's composite method: 0.001118 Simpson's composite method: 0.001136 Simpson's composite method: 0.001154 Simpson's composite method: 0.001172 Simpson's composite method: 0.001191 Simpson's composite method: 0.001209 Simpson's composite method: 0.001228 Simpson's composite method: 0.001247 Simpson's composite method: 0.001266 Simpson's composite method: 0.001285 Simpson's composite method: 0.001305 Simpson's composite method: 0.001325 Simpson's composite method: 0.001344 Simpson's composite method: 0.001364 Simpson's composite method: 0.001384 Simpson's composite method: 0.001404 Simpson's composite method: 0.001425 Simpson's composite method: 0.001445 Simpson's composite method: 0.001466 Simpson's composite method: 0.001487 Simpson's composite method: 0.001508 Simpson's composite method: 0.001529 Simpson's composite method: 0.001550 Simpson's composite method: 0.001572 Simpson's composite method: 0.001593 Simpson's composite method: 0.001615 Simpson's composite method: 0.001636 Simpson's composite method: 0.001658 Simpson's composite method: 0.001680 Simpson's composite method: 0.001703 Simpson's composite method: 0.001725 Simpson's composite method: 0.001747 Simpson's composite method: 0.001770 Simpson's composite method: 0.001792 Simpson's composite method: 0.001815 Simpson's composite method: 0.001838 Simpson's composite method: 0.001861 Simpson's composite method: 0.001884 Simpson's composite method: 0.001907 Simpson's composite method: 0.001930 Simpson's composite method: 0.001954 Simpson's composite method: 0.001977 Simpson's composite method: 0.002000 Simpson's composite method: 0.002024 Simpson's composite method: 0.002048 Simpson's composite method: 0.002071 Simpson's composite method: 0.002095 Simpson's composite method: 0.002119 Simpson's composite method: 0.002143 Simpson's composite method: 0.002167 Simpson's composite method: 0.002191 Simpson's composite method: 0.002215 Simpson's composite method: 0.002239 Simpson's composite method: 0.002263 Simpson's composite method: 0.002287 Simpson's composite method: 0.002311 Simpson's composite method: 0.002335 Simpson's composite method: 0.002359 Simpson's composite method: 0.002383 Simpson's composite method: 0.002408 Simpson's composite method: 0.002432 Simpson's composite method: 0.002456 Simpson's composite method: 0.002480 Simpson's composite method: 0.002504 Simpson's composite method: 0.002529 Simpson's composite method: 0.002553 Simpson's composite method: 0.002577 Simpson's composite method: 0.002601 Simpson's composite method: 0.002625 Simpson's composite method: 0.002649 Simpson's composite method: 0.002673 Simpson's composite method: 0.002697 Simpson's composite method: 0.002721 Simpson's composite method: 0.002744 Simpson's composite method: 0.002768 Simpson's composite method: 0.002792 Simpson's composite method: 0.002815 Simpson's composite method: 0.002839 Simpson's composite method: 0.002862 Simpson's composite method: 0.002885 Simpson's composite method: 0.002908 Simpson's composite method: 0.002932 Simpson's composite method: 0.002955 Simpson's composite method: 0.002977 Simpson's composite method: 0.003000 Simpson's composite method: 0.003023 Simpson's composite method: 0.003045 Simpson's composite method: 0.003067 Simpson's composite method: 0.003090 Simpson's composite method: 0.003112 Simpson's composite method: 0.003133 Simpson's composite method: 0.003155 Simpson's composite method: 0.003177 Simpson's composite method: 0.003198 Simpson's composite method: 0.003219 Simpson's composite method: 0.003240 Simpson's composite method: 0.003261 Simpson's composite method: 0.003282 Simpson's composite method: 0.003302 Simpson's composite method: 0.003322 Simpson's composite method: 0.003342 Simpson's composite method: 0.003362 Simpson's composite method: 0.003382 Simpson's composite method: 0.003401 Simpson's composite method: 0.003420 Simpson's composite method: 0.003439 Simpson's composite method: 0.003457 Simpson's composite method: 0.003476 Simpson's composite method: 0.003494 Simpson's composite method: 0.003512 Simpson's composite method: 0.003529 Simpson's composite method: 0.003547 Simpson's composite method: 0.003564 Simpson's composite method: 0.003581 Simpson's composite method: 0.003597 Simpson's composite method: 0.003613 Simpson's composite method: 0.003629 Simpson's composite method: 0.003645 Simpson's composite method: 0.003660 Simpson's composite method: 0.003675 Simpson's composite method: 0.003690 Simpson's composite method: 0.003704 Simpson's composite method: 0.003719 Simpson's composite method: 0.003732 Simpson's composite method: 0.003746 Simpson's composite method: 0.003759 Simpson's composite method: 0.003772 Simpson's composite method: 0.003784 Simpson's composite method: 0.003796 Simpson's composite method: 0.003808 Simpson's composite method: 0.003820 Simpson's composite method: 0.003831 Simpson's composite method: 0.003841 Simpson's composite method: 0.003852 Simpson's composite method: 0.003862 Simpson's composite method: 0.003871 Simpson's composite method: 0.003881 Simpson's composite method: 0.003890 Simpson's composite method: 0.003898 Simpson's composite method: 0.003906 Simpson's composite method: 0.003914 Simpson's composite method: 0.003922 Simpson's composite method: 0.003929 Simpson's composite method: 0.003935 Simpson's composite method: 0.003942 Simpson's composite method: 0.003948 Simpson's composite method: 0.003953 Simpson's composite method: 0.003958 Simpson's composite method: 0.003963 Simpson's composite method: 0.003967 Simpson's composite method: 0.003971 Simpson's composite method: 0.003975 Simpson's composite method: 0.003978 Simpson's composite method: 0.003981 Simpson's composite method: 0.003983 Simpson's composite method: 0.003985 Simpson's composite method: 0.003987 Simpson's composite method: 0.003988 Simpson's composite method: 0.003989 Simpson's composite method: 0.003989 Simpson's composite method: 0.003989 Simpson's composite method: 0.003989 Simpson's composite method: 0.003988 Simpson's composite method: 0.003987 Simpson's composite method: 0.003985 Simpson's composite method: 0.003983 Simpson's composite method: 0.003981 Simpson's composite method: 0.003978 Simpson's composite method: 0.003975 Simpson's composite method: 0.003971 Simpson's composite method: 0.003967 Simpson's composite method: 0.003963 Simpson's composite method: 0.003958 Simpson's composite method: 0.003953 Simpson's composite method: 0.003948 Simpson's composite method: 0.003942 Simpson's composite method: 0.003935 Simpson's composite method: 0.003929 Simpson's composite method: 0.003922 Simpson's composite method: 0.003914 Simpson's composite method: 0.003906 Simpson's composite method: 0.003898 Simpson's composite method: 0.003890 Simpson's composite method: 0.003881 Simpson's composite method: 0.003871 Simpson's composite method: 0.003862 Simpson's composite method: 0.003852 Simpson's composite method: 0.003841 Simpson's composite method: 0.003831 Simpson's composite method: 0.003820 Simpson's composite method: 0.003808 Simpson's composite method: 0.003796 Simpson's composite method: 0.003784 Simpson's composite method: 0.003772 Simpson's composite method: 0.003759 Simpson's composite method: 0.003746 Simpson's composite method: 0.003732 Simpson's composite method: 0.003719 Simpson's composite method: 0.003704 Simpson's composite method: 0.003690 Simpson's composite method: 0.003675 Simpson's composite method: 0.003660 Simpson's composite method: 0.003645 Simpson's composite method: 0.003629 Simpson's composite method: 0.003613 Simpson's composite method: 0.003597 Simpson's composite method: 0.003581 Simpson's composite method: 0.003564 Simpson's composite method: 0.003547 Simpson's composite method: 0.003529 Simpson's composite method: 0.003512 Simpson's composite method: 0.003494 Simpson's composite method: 0.003476 Simpson's composite method: 0.003457 Simpson's composite method: 0.003439 Simpson's composite method: 0.003420 Simpson's composite method: 0.003401 Simpson's composite method: 0.003382 Simpson's composite method: 0.003362 Simpson's composite method: 0.003342 Simpson's composite method: 0.003322 Simpson's composite method: 0.003302 Simpson's composite method: 0.003282 Simpson's composite method: 0.003261 Simpson's composite method: 0.003240 Simpson's composite method: 0.003219 Simpson's composite method: 0.003198 Simpson's composite method: 0.003177 Simpson's composite method: 0.003155 Simpson's composite method: 0.003133 Simpson's composite method: 0.003112 Simpson's composite method: 0.003090 Simpson's composite method: 0.003067 Simpson's composite method: 0.003045 Simpson's composite method: 0.003023 Simpson's composite method: 0.003000 Simpson's composite method: 0.002977 Simpson's composite method: 0.002955 Simpson's composite method: 0.002932 Simpson's composite method: 0.002908 Simpson's composite method: 0.002885 Simpson's composite method: 0.002862 Simpson's composite method: 0.002839 Simpson's composite method: 0.002815 Simpson's composite method: 0.002792 Simpson's composite method: 0.002768 Simpson's composite method: 0.002744 Simpson's composite method: 0.002721 Simpson's composite method: 0.002697 Simpson's composite method: 0.002673 Simpson's composite method: 0.002649 Simpson's composite method: 0.002625 Simpson's composite method: 0.002601 Simpson's composite method: 0.002577 Simpson's composite method: 0.002553 Simpson's composite method: 0.002529 Simpson's composite method: 0.002504 Simpson's composite method: 0.002480 Simpson's composite method: 0.002456 Simpson's composite method: 0.002432 Simpson's composite method: 0.002408 Simpson's composite method: 0.002383 Simpson's composite method: 0.002359 Simpson's composite method: 0.002335 Simpson's composite method: 0.002311 Simpson's composite method: 0.002287 Simpson's composite method: 0.002263 Simpson's composite method: 0.002239 Simpson's composite method: 0.002215 Simpson's composite method: 0.002191 Simpson's composite method: 0.002167 Simpson's composite method: 0.002143 Simpson's composite method: 0.002119 Simpson's composite method: 0.002095 Simpson's composite method: 0.002071 Simpson's composite method: 0.002048 Simpson's composite method: 0.002024 Simpson's composite method: 0.002000 Simpson's composite method: 0.001977 Simpson's composite method: 0.001954 Simpson's composite method: 0.001930 Simpson's composite method: 0.001907 Simpson's composite method: 0.001884 Simpson's composite method: 0.001861 Simpson's composite method: 0.001838 Simpson's composite method: 0.001815 Simpson's composite method: 0.001792 Simpson's composite method: 0.001770 Simpson's composite method: 0.001747 Simpson's composite method: 0.001725 Simpson's composite method: 0.001703 Simpson's composite method: 0.001680 Simpson's composite method: 0.001658 Simpson's composite method: 0.001636 Simpson's composite method: 0.001615 Simpson's composite method: 0.001593 Simpson's composite method: 0.001572 Simpson's composite method: 0.001550 Simpson's composite method: 0.001529 Simpson's composite method: 0.001508 Simpson's composite method: 0.001487 Simpson's composite method: 0.001466 Simpson's composite method: 0.001445 Simpson's composite method: 0.001425 Simpson's composite method: 0.001404 Simpson's composite method: 0.001384 Simpson's composite method: 0.001364 Simpson's composite method: 0.001344 Simpson's composite method: 0.001325 Simpson's composite method: 0.001305 Simpson's composite method: 0.001285 Simpson's composite method: 0.001266 Simpson's composite method: 0.001247 Simpson's composite method: 0.001228 Simpson's composite method: 0.001209 Simpson's composite method: 0.001191 Simpson's composite method: 0.001172 Simpson's composite method: 0.001154 Simpson's composite method: 0.001136 Simpson's composite method: 0.001118 Simpson's composite method: 0.001100 Simpson's composite method: 0.001083 Simpson's composite method: 0.001065 Simpson's composite method: 0.001048 Simpson's composite method: 0.001031 Simpson's composite method: 0.001014 Simpson's composite method: 0.000998 Simpson's composite method: 0.000981 Simpson's composite method: 0.000965 Simpson's composite method: 0.000949 Simpson's composite method: 0.000933 Simpson's composite method: 0.000917 Simpson's composite method: 0.000901 Simpson's composite method: 0.000886 Simpson's composite method: 0.000870 Simpson's composite method: 0.000855 Simpson's composite method: 0.000840 Simpson's composite method: 0.000826 Simpson's composite method: 0.000811 Simpson's composite method: 0.000797 Simpson's composite method: 0.000782 Simpson's composite method: 0.000768 Simpson's composite method: 0.000755 Simpson's composite method: 0.000741 Simpson's composite method: 0.000727 Simpson's composite method: 0.000714 Simpson's composite method: 0.000701 Simpson's composite method: 0.000688 Simpson's composite method: 0.000675 Simpson's composite method: 0.000662 Simpson's composite method: 0.000650 Simpson's composite method: 0.000638 Simpson's composite method: 0.000626 Simpson's composite method: 0.000614 Simpson's composite method: 0.000602 Simpson's composite method: 0.000590 Simpson's composite method: 0.000579 Simpson's composite method: 0.000567 Simpson's composite method: 0.000556 Simpson's composite method: 0.000545 Simpson's composite method: 0.000535 Simpson's composite method: 0.000524 Simpson's composite method: 0.000513 Simpson's composite method: 0.000503 Simpson's composite method: 0.000493 Simpson's composite method: 0.000483 Simpson's composite method: 0.000473 Simpson's composite method: 0.000463 Simpson's composite method: 0.000454 Simpson's composite method: 0.000444 Simpson's composite method: 0.000435 Simpson's composite method: 0.000426 Simpson's composite method: 0.000417 Simpson's composite method: 0.000408 Simpson's composite method: 0.000400 Simpson's composite method: 0.000391 Simpson's composite method: 0.000383 Simpson's composite method: 0.000375 Simpson's composite method: 0.000367 Simpson's composite method: 0.000359 Simpson's composite method: 0.000351 Simpson's composite method: 0.000343 Simpson's composite method: 0.000336 Simpson's composite method: 0.000328 Simpson's composite method: 0.000321 Simpson's composite method: 0.000314 Simpson's composite method: 0.000307 Simpson's composite method: 0.000300 Simpson's composite method: 0.000293 Simpson's composite method: 0.000287 Simpson's composite method: 0.000280 Simpson's composite method: 0.000274 Simpson's composite method: 0.000267 Simpson's composite method: 0.000261 Simpson's composite method: 0.000255 Simpson's composite method: 0.000249 Simpson's composite method: 0.000243 Simpson's composite method: 0.000238 Simpson's composite method: 0.000232 Simpson's composite method: 0.000227 Simpson's composite method: 0.000221 Simpson's composite method: 0.000216 Simpson's composite method: 0.000211 Simpson's composite method: 0.000206 Simpson's composite method: 0.000201 Simpson's composite method: 0.000196 Simpson's composite method: 0.000191 Simpson's composite method: 0.000187 Simpson's composite method: 0.000182 Simpson's composite method: 0.000177 Simpson's composite method: 0.000173 Simpson's composite method: 0.000169 Simpson's composite method: 0.000165 Simpson's composite method: 0.000161 Simpson's composite method: 0.000156 Simpson's composite method: 0.000153 Simpson's composite method: 0.000149 Simpson's composite method: 0.000145 Simpson's composite method: 0.000141 Simpson's composite method: 0.000138 Simpson's composite method: 0.000134 Simpson's composite method: 0.000131 Simpson's composite method: 0.000127 Simpson's composite method: 0.000124 Simpson's composite method: 0.000121 Simpson's composite method: 0.000118 Simpson's composite method: 0.000114 Simpson's composite method: 0.000111 Simpson's composite method: 0.000109 Simpson's composite method: 0.000106 Simpson's composite method: 0.000103 Simpson's composite method: 0.000100 Simpson's composite method: 0.000097 Simpson's composite method: 0.000095 Simpson's composite method: 0.000092 Simpson's composite method: 0.000090 Simpson's composite method: 0.000087 Simpson's composite method: 0.000085 Simpson's composite method: 0.000083 Simpson's composite method: 0.000080 Simpson's composite method: 0.000078 Simpson's composite method: 0.000076 Simpson's composite method: 0.000074 Simpson's composite method: 0.000072 Simpson's composite method: 0.000070 Simpson's composite method: 0.000068 Simpson's composite method: 0.000066 Simpson's composite method: 0.000064 Simpson's composite method: 0.000062 Simpson's composite method: 0.000060 Simpson's composite method: 0.000059 Simpson's composite method: 0.000057 Simpson's composite method: 0.000055 Simpson's composite method: 0.000054 Simpson's composite method: 0.000052 Simpson's composite method: 0.000051 Simpson's composite method: 0.000049 Simpson's composite method: 0.000048 Simpson's composite method: 0.000046 Simpson's composite method: 0.000045 Simpson's composite method: 0.000044 Simpson's composite method: 0.000042 Simpson's composite method: 0.000041 Simpson's composite method: 0.000040 Simpson's composite method: 0.000039 Simpson's composite method: 0.000038 Simpson's composite method: 0.000036 Simpson's composite method: 0.000035 Simpson's composite method: 0.000034 Simpson's composite method: 0.000033 Simpson's composite method: 0.000032 Simpson's composite method: 0.000031 Simpson's composite method: 0.000030 Simpson's composite method: 0.000029 Simpson's composite method: 0.000028 Simpson's composite method: 0.000028 Simpson's composite method: 0.000027 Simpson's composite method: 0.000026 Simpson's composite method: 0.000025 Simpson's composite method: 0.000024 Simpson's composite method: 0.000023 Simpson's composite method: 0.000023 Simpson's composite method: 0.000022 Simpson's composite method: 0.000021 Simpson's composite method: 0.000021 Simpson's composite method: 0.000020 Simpson's composite method: 0.000019 Simpson's composite method: 0.000019 Simpson's composite method: 0.000018 Simpson's composite method: 0.000018 Simpson's composite method: 0.000017 Simpson's composite method: 0.000016 Simpson's composite method: 0.000016 Simpson's composite method: 0.000015 Simpson's composite method: 0.000015 Simpson's composite method: 0.000014 Simpson's composite method: 0.000014 Simpson's composite method: 0.000013 Simpson's composite method: 0.000013 Simpson's composite method: 0.000013 Simpson's composite method: 0.000012 Simpson's composite method: 0.000012 Simpson's composite method: 0.000011 Simpson's composite method: 0.000011 Simpson's composite method: 0.000011 Simpson's composite method: 0.000010 Simpson's composite method: 0.000010 Simpson's composite method: 0.000010 Simpson's composite method: 0.000009 Simpson's composite method: 0.000009 Simpson's composite method: 0.000009 Simpson's composite method: 0.000008 Simpson's composite method: 0.000008 Simpson's composite method: 0.000008 Simpson's composite method: 0.000007 Simpson's composite method: 0.000007 Simpson's composite method: 0.000007 Simpson's composite method: 0.000007 Simpson's composite method: 0.000006 Simpson's composite method: 0.000006 Simpson's composite method: 0.000006 Simpson's composite method: 0.000006 Simpson's composite method: 0.000006 Simpson's composite method: 0.000005 Simpson's composite method: 0.000005 Simpson's composite method: 0.000005 Simpson's composite method: 0.000005 Simpson's composite method: 0.000005 Simpson's composite method: 0.000004 Simpson's composite method: 0.000004 Simpson's composite method: 0.000004 Simpson's composite method: 0.000004 Simpson's composite method: 0.000004 Simpson's composite method: 0.000004 Simpson's composite method: 0.000004 Simpson's composite method: 0.000003 Simpson's composite method: 0.000003 Simpson's composite method: 0.000003 Simpson's composite method: 0.000003 Simpson's composite method: 0.000003 Simpson's composite method: 0.000003 Simpson's composite method: 0.000003 Simpson's composite method: 0.000003 Simpson's composite method: 0.000003 Simpson's composite method: 0.000002 Simpson's composite method: 0.000002 Simpson's composite method: 0.000002 Simpson's composite method: 0.000002 Simpson's composite method: 0.000002 Simpson's composite method: 0.000002 Simpson's composite method: 0.000002 Simpson's composite method: 0.000002 Simpson's composite method: 0.000002 Simpson's composite method: 0.000002 Simpson's composite method: 0.000002 Simpson's composite method: 0.000002 Simpson's composite method: 0.000002 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000001 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000 Simpson's composite method: 0.000000

fprintf('Exact value: %f\n', norm_exact);

Exact value: 1.000000

% Plot the approximations and the exact values

figure;

subplot(2,1,1);

length(x)

ans = 2001

length(f_t(x, 10))

ans = 2001

length(x(1:end-1))

ans = 2000

length(t_trap)

ans = 1000

length(x(1:2:end))

ans = 1001

length(t_simp)

ans = 1000

plot(x, f_t(x, 10), 'k', x(1:end-1), t_trap, 'r', x(1:2:end), t_simp, 'b--');

Error using plot
Vectors must be the same length.

legend('Exact', 'Trapezoid', 'Simpson''s');

title('T-distribution Probability Density Function');

subplot(2,1,2);

plot(x, f_norm(x), 'k', x(1:end-1), norm_trap, 'r', x(1:2:end), norm_simp, 'b--');

legend('Exact', 'Trapezoid', 'Simpson''s');

title('Normal Distribution Probability Density Function');

2 comentarios
Mostrar NingunoOcultar Ninguno

Shoaib Salim el 6 de Abr. de 2023

How can i edit to get rid of this error as i tried above mentioned steps but not succeeded

Oguz Kaan Hancioglu el 7 de Abr. de 2023

Abrir en MATLAB Online

it is caused by you assigning the same variable name different array.

x = linspace(a, b, n+1); % length of x = 1001
t_trap = h/2 * (f_t(x(1:end-1), 10) + f_t(x(2:end), 10)); % length of t_trap 1001
norm_trap = h/2 * (f_norm(x(1:end-1)) + f_norm(x(2:end)));
% Use Simpson's composite method to approximate the integrals
x = linspace(a, b, 2*n+1); % length of x 2001
% now length of x = 2001 but t_trap = 1001
plot(x, f_t(x, 10), 'k', x(1:end-1), t_trap, 'r', x(1:2:end), t_simp, 'b--');

plesae assign different names for x arrays.

Iniciar sesión para comentar.

Answer 2

Joe Vinciguerra el 6 de Abr. de 2023

0
Enlazar

Enlace directo a esta respuesta

https://es.mathworks.com/matlabcentral/answers/1942789-numerical-method-matlab-code#answer_1211059

Abrir en MATLAB Online

The x and y vectors for a plot need to be the same length. You were close, but looks like you had a typo. Try this:

% Plot the approximations and the exact values
figure;
subplot(2,1,1);
% plot(x, f_t(x, 10), 'k', x(1:end-1), t_trap, 'r', x(1:2:end), t_simp, 'b--');
plot(x, f_t(x, 10), 'k', x(1:2:end-1), t_trap, 'r', x(1:2:end-1), t_simp, 'b--');
legend('Exact', 'Trapezoid', 'Simpson''s');
title('T-distribution Probability Density Function');
subplot(2,1,2);
% plot(x, f_norm(x), 'k', x(1:end-1), norm_trap, 'r', x(1:2:end), norm_simp, 'b--');
plot(x, f_norm(x), 'k', x(1:2:end-1), norm_trap, 'r', x(1:2:end-1), norm_simp, 'b--');
legend('Exact', 'Trapezoid', 'Simpson''s');
title('Normal Distribution Probability Density Function');

For more details: 2-D line plot - MATLAB plot (mathworks.com)

1 comentario
Mostrar -1 comentarios más antiguosOcultar -1 comentarios más antiguos

Shoaib Salim el 6 de Abr. de 2023

I tried this earlier but it does not make sense in plot

Iniciar sesión para comentar.

Numerical method MATLAB code

7 comentarios
Mostrar 5 comentarios más antiguosOcultar 5 comentarios más antiguos

Respuesta aceptada

2 comentarios
Mostrar NingunoOcultar Ninguno

Más respuestas (1)

1 comentario
Mostrar -1 comentarios más antiguosOcultar -1 comentarios más antiguos

Ver también

Categorías

Etiquetas

Community Treasure Hunt

Numerical method MATLAB code

7 comentarios Mostrar 5 comentarios más antiguosOcultar 5 comentarios más antiguos

Respuesta aceptada

2 comentarios Mostrar NingunoOcultar Ninguno

Más respuestas (1)

1 comentario Mostrar -1 comentarios más antiguosOcultar -1 comentarios más antiguos

Ver también

Categorías

Etiquetas

Community Treasure Hunt

7 comentarios
Mostrar 5 comentarios más antiguosOcultar 5 comentarios más antiguos

2 comentarios
Mostrar NingunoOcultar Ninguno

1 comentario
Mostrar -1 comentarios más antiguosOcultar -1 comentarios más antiguos