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Math Help - Complex plane integrals

  1. #1
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    Complex plane integrals

    1) \oint_{\mid z+1\mid =1}\frac{dz}{z^{2}-1}
    2) \oint_{\mid z-i\mid =2}\frac{sin(\pi z)}{z^{4}}dz
    3) \int_{0}^{\pi}\frac{d \theta}{2+cos(\theta)}
    4) \int_{- \infty}^{\infty}\frac{cos(x)}{x^{4}+1}dx

    Can you please tell me how can I find the value of these integrals? Just tell me how.
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  2. #2
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  3. #3
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    Re: Complex plane integrals

    Are you sure? I think I should use Cauchy's residue theorem and Laurent series for 1), 2) and 4).

    Cauchy's integral formula can be used for integrals like: \oint_{\gamma} \frac{f(z)}{{(z-a)}^{n}}dz
    Last edited by cristi92; March 27th 2012 at 02:25 AM.
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