mid-point method Integration

Question

Tony 2014-1-4

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回答： Akshay satpute 2017-10-8

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Find numerically , to a 1/10000 accuracy, the values of the following definite integral:

0 to inf 1/(x^2+1) dx

use the mid-point method.

not show how to answer this i went about integrating it. My knowledge of the midpoint rule is limited.

the width of the sub intervals would be 1/10000 but how would you go about dividing it by infinity. I did the integration:

if true
  % code
syms x
a1= int(1/(x^2+1),x,0,inf)
end

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John D'Errico 2014-1-5

Why do you think you need an "if true" in there??????

Youssef Khmou 2014-1-5

the instruction if true appeared because the poster clicked on "Code" button

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Answer 1

Youssef Khmou 2014-1-5

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/111430-mid-point-method-integration#answer_120050

在 MATLAB Online 中打开

Theoretically that integral equals pi/2, here is version, try to adjust it :

% MidPoint test integration
clear;
f=inline('1./((x.^2)+1)');
N=20000;
dx=1/1e+2;
F=0;
x1=0;
for t=1:N
  xi=(dx/2)+x1;
  F=F+dx*f(xi);
  x1=x1+dx;
end

% For verification try :

quad(f,0,1e+18)

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Tony 2014-1-5

thank you for your time question. N should equal 10000 no? and dx=1/100 right? just don't understand why dx is 1/100.

trying to understand since i don't fairly understand the midpoint rule. it should be something like ((b-a)/subintervals) * f(x1)+f(x2)...f(xn). I don't see how it fits in that general form

Youssef Khmou 2014-1-5