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Math Help - Integration and complex nos

  1. #1
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    Integration and complex nos

    Can someone help me please

    Thanx
    Edgar



    a)Evaluate the integral

    integral from minus infintiy to infinity of 1/(1+x)^4 dx

    b)Where are the poles of 1/(1+z)^4 ?
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  2. #2
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    Quote Originally Posted by edgar davids View Post

    a)Evaluate the integral

    integral from minus infintiy to infinity of 1/(1+x)^4 dx
    You need to find,
    \int_{\infty}^{\infty} \frac{1}{(1+x)^4}dx
    The function has a vertical asymptote at x=-1
    Thus you need to do,
    \int_{-\infty}^{-1^-} \frac{1}{(1+x)^4} dx+\int_{-1^+}^{\infty} \frac{1}{(1+x)^4} dx
    Which is,
     (-1/5)(1+x)^{-5}|_{-\infty}^{-1^-}+(-1/5)(1+x)^{-5}|_{-1^+}^{\infty}
    That looks unbounded to me.
    b)Where are the poles of 1/(1+z)^4 ?
    z=-1 of order 4.
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