# mid-point method Integration

8 views (last 30 days)
Tony on 4 Jan 2014
Answered: Akshay satpute on 8 Oct 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 CommentsShow 1 older commentHide 1 older comment
Youssef Khmou on 5 Jan 2014
the instruction if true appeared because the poster clicked on "Code" button

Youssef Khmou on 5 Jan 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 :
##### 2 CommentsShow 1 older commentHide 1 older comment
Youssef Khmou on 5 Jan 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

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

### Categories

Find more on Partial Differential Equation Toolbox in Help Center and File Exchange

### Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by