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A small problem with a complex integral

  1. Apr 7, 2010 #1
    Hi...

    I have an integral over a contour. The contour is a semicircle with vanishing radius around the origin and situated in the upper half plane.

    The integrand is [tex]\frac{(lnx)^2}{1+x^2}[/tex].

    The integral is supposed be zero.


    I don't see how. Taking the modulus and letting the radius go to zero, I find that the denominator goes to 1 and the numerator is of the form [tex]ln(r^2)+\theta^2[/tex] with r going to zero.

    Can anybody tell me what I might be missing?
     
  2. jcsd
  3. Apr 7, 2010 #2

    tiny-tim

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    hi krishna! :smile:

    but the arc-length is πr, so you multiply by that :wink:
     
  4. Apr 8, 2010 #3
    Yep..thanks a lot tiny tim!:smile:
     
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