
a tough integral
Hey guys.
I have this problem:
http://img12.imageshack.us/img12/6729/91881544.jpg
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.

When x is small, sin(x)/x is close to 1. So you are integrating a function that is approximately 1 over a very short interval (of length πε), and the integral will be small, tending to 0 as ε→0. Another way to see this is to notice that the singularity at 0 is removable, so what happens near it does not really affect the integral.