1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Indented Contour Integral

  1. Oct 9, 2008 #1
    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
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?



Similar Discussions: Indented Contour Integral
  1. Line Integrals (Replies: 0)

  2. Simplifying Integral (Replies: 0)

  3. Several Integrals (Replies: 0)

  4. Complex integral (Replies: 0)

Loading...