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mid-point method Integration

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Tony
Tony il 4 Gen 2014
Risposto: Akshay satpute il 8 Ott 2017
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
  2 Commenti
John D'Errico
John D'Errico il 5 Gen 2014
Why do you think you need an "if true" in there??????
Youssef  Khmou
Youssef Khmou il 5 Gen 2014
the instruction if true appeared because the poster clicked on "Code" button

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Risposte (2)

Youssef  Khmou
Youssef Khmou il 5 Gen 2014
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)
  2 Commenti
Tony
Tony il 5 Gen 2014
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
Youssef Khmou il 5 Gen 2014
dx was taken arbitrarily, try with dx=1e-4 . that code is based on the formula in this file, try to look at this file first

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Akshay satpute
Akshay satpute il 8 Ott 2017
tell me program of integration of {x^2 (sinh(X)+cosh(x))dx} between limit 0 to 1 in 100 parts

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