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Residue theorem

  1. Jun 14, 2012 #1
    1. The problem statement, all variables and given/known data
    integrate x^0.5/(1+x^2) by using complex integration


    2. Relevant equations

    residue theorem

    3. The attempt at a solution
    my attempt at a solution is attached.i need help in finding where am i mistaken.
    thank's
    Hedi
     

    Attached Files:

    • 001.jpg
      001.jpg
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    • 002.jpg
      002.jpg
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  2. jcsd
  3. Jun 14, 2012 #2
    . . . that's too messy to read. For me at least. Try and learn the math formatting language Latex to nicely format your math. Is this what you want to integrate:

    [tex]\int_0^{\infty} \frac{\sqrt{x}}{1+x^2}dx[/tex]

    If so, how about taking a half-disc contour in the upper half-plane, indented around the branch-point at the origin. For now, just suppose the small and large half-circle contours go to zero and you're left with the two legs on the real axis. Then the integral over those two legs is equal to 2pi i times the residue at i right.
     
  4. Jun 14, 2012 #3
    Thank you, that works.
     
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