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Math Help - evaluating an integral

  1. #1
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    evaluating an integral

    does anybody know how to evaluate this integral ?

    evaluating an integral-delete.bmp

    thank you for you help
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  2. #2
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    Quote Originally Posted by PeaceSoul View Post
    does anybody know how to evaluate this integral ?

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    thank you for you help
    Use the residue theorem! You will have two cases

    Case 1:

    if p(b)=0 then the residue at b is given by

    \displaystyle \text{Res}(f,z=b)=\lim_{z \to b}(z-b)\frac{p(z)}{z-b}=0

    if p(b)=a then the residue at b is given by

    \displaystyle \text{Res}(f,z=b)=\lim_{z \to b}(z-b)\frac{p(z)}{z-b}=p(b)

    so by the residue theorem \displaystyle \int_c \frac{p(z)}{z-b}dz=2\pi i \text{Res}(f,z=b)=2 \pi i p(b)
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  3. #3
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    thank you SO much
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