Originally Posted by
lilyungn I need help computing this integral with the different techniques mentioned below.
∫ 50 1/x dx
1
(thats a 50 at the top and a 1 at the bottom of the integram sign)
- Right rectangular scheme
- Left rectangular scheme
- Midpoint Rectangular scheme
- trapezoid scheme
- Simpson sRule
for the first 2 just use the definition of a Riemann sum.
Here is some pseudo code
if you want left end points and for right
Now for the left just calculate
.
In Matlab would use parameters like a and b and have the function take them as an input. Also if you define your partition as a vector you can have Matlab evaluate all of the 's at the same time. Just modify the above to use the other quadrature rules.
Here is a copy of an m file for the left end point
Code:
function [ output ] = LeftEnd(n,a,b )
%Use Left end point to approximate the integral of 1/x from a to b using
% n points.
OneOver=@(x) x.^(-1);
v=zeros(1,n);
for m=1:n
v(1,m)=a+((b-a)/n)*((m-1));
end
y=OneOver(v);
output=((b-a)/n)*sum(y);
end