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Math Help - Complex Contour Integration With Branch Cut

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    Complex Contour Integration With Branch Cut

    Hi i'm stuck on a problem and was wondering if anyone could help. The problem is as follows:

    "It is required to evaluate
    L=\int_{- \ 1}^{1}\frac {({1-x^2})^\frac{1}{2}}{1+x^2}dx,
    using contour integration.

    a) consider the function f(z)=\frac {({z^2-1})^\frac{1}{2}}{z^2+1}
    (You are given that, with -\pi<\arg(z\pm1)\leq\pi, the only branch cut needed is the section [-1,1] of the real axis)

    i)Find the value of M=\oint f(z)dz around a circle of large radius.
    ii)Relate M to the value of N=\oint f(z)dz around the cut.
    iii)Express N in terms of L, and hence evaluate L."

    Thanks for reading.
    Last edited by TSVenture; December 9th 2010 at 10:57 AM. Reason: removed dz from line a) consider.....
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