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Math Help - solving integral problem by complex analysis method

  1. #1
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    solving integral problem by complex analysis method

    I got this problem to solve but have no much confidence in my solution. Can anyone help me. Thanks in advance.
    Attached Thumbnails Attached Thumbnails solving integral problem by complex analysis method-hw1-1.png  
    Last edited by firebird; July 27th 2011 at 11:37 PM.
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    Re: solving integral problem by complex analysis method

    Anyone?
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  3. #3
    MHF Contributor FernandoRevilla's Avatar
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    Re: solving integral problem by complex analysis method

    Quote Originally Posted by firebird View Post
    Anyone?
    Always there is someone. You have correctly found CPV=\lim_{R\to +\infty}\int_{-R}^Rf(x)\;dx (Cauchy Principal Value). As the given integral is convergent then, \int_{-\infty}^{+\infty}f(x)\;dx=CPV=\pi/\sqrt{2}
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    Re: solving integral problem by complex analysis method

    Quote Originally Posted by FernandoRevilla View Post
    Always there is someone. You have correctly found CPV=\lim_{R\to +\infty}\int_{-R}^Rf(x)\;dx (Cauchy Principal Value). As the given integral is convergent then, \int_{-\infty}^{+\infty}f(x)\;dx=CPV=\pi/\sqrt{2}
    Thank you very much.
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  5. #5
    MHF Contributor FernandoRevilla's Avatar
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    Re: solving integral problem by complex analysis method

    Quote Originally Posted by firebird View Post
    Thank you very much.
    You are welcome.
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