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Homework Help: Branch Cuts and Integral Evaluation

  1. Feb 9, 2010 #1
    1. The problem statement, all variables and given/known data

    The function f(z) = (1-z2)1/2 of complex variable z is defined to be real and positive in the range -1 < z < 1. Using cuts running along the real axis for 1 < x < infinity and -infinity < x < -1, show how f(z) is made single valued and evaluate it on the upper and lower sides of both cuts.

    Use these results and a suitable contour in the complex plane to evaluate the integral of:

    (dx)/(x(x2 - 1)1/2)

    from 1 to infinity


    3. The attempt at a solution

    I've gotten the first part of the problem, but I'm not sure how to apply that to the integral. I've attached my work so that you know I've actually done something, but I'm confused as to how I use that work to help with solving that integral.
     

    Attached Files:

  2. jcsd
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