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Homework Help: 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
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