# Indented Contour Integral

1. Oct 9, 2008

### JohnSimpson

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

Use contour integration to obtain the result int(sin(x)^2/x^2, x=-Inf..Inf) = Pi

2. Relevant equations

3. The attempt at a solution

I defined a contour that encircles the pole at z=0. It looks like a bridge over the pole. The outer integral is easily shown to be zero, and the two along the x axis converge to the integral of interest. Every time I do the small integral around the pole, the integrand blows up as a i tend the radius to zero.

Note that the lemma typically used to evaluate integrals such as sinx/x is not valid because z=0 is not a simple pole.

Any help would be appreciated