# Homework Help: A tough integral

1. Mar 10, 2009

### asi123

1. The problem statement, all variables and given/known data

Hey guys.

I have this problem:

http://img12.imageshack.us/img12/6729/91881544.jpg [Broken]

It's like a two parts problem.
The first one was to prove the equation in red, I did that with a bit of trigo.
The second part is to use the integral of the function in green to prove the thing in yellow. I'm stuck on the path that goes from - epsilon to epsilon, that semi circle, how can I find the value of this function on the path?

Thanks.

2. Relevant equations

3. The attempt at a solution

Last edited by a moderator: May 4, 2017
2. Mar 10, 2009

### yyat

Compute the http://en.wikipedia.org/wiki/Residue_(complex_analysis)" [Broken] of f at zero, the use

$$2\pi iRes(f,0)=\int_{|z|=\epsilon}f(z)dz$$

and try to find the integral over the half-circle in terms of the integral over the entire circle.

Last edited by a moderator: May 4, 2017