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Small mistake, complex calculus

  1. Oct 21, 2009 #1
    Im trying to solve:
    But i always come out:
    [tex]\int^{2PI}_{0}[/tex] (sin²(x) / (5 - 4cos(x))dx

    ==> (i/4)[tex]\oint(z^2-1)^2 / (z^2(z-2)(z-1/2)) dz[/tex]

    = 2pi i (i/4) (RES (z=0) + RES (z = 1/2)) = (-pi/2) (5/2 - 3/2) = -pi/2

    instead of pi/4 please help
  2. jcsd
  3. Oct 21, 2009 #2


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    I can't really tell what you are doing wrong from what you've posted, but I get a factor of (-i/8) in front of your contour integral.
  4. Oct 21, 2009 #3
    That would do the trick, but could you please write how you get to -i/8 in front of it ?
  5. Oct 21, 2009 #4


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    How did you get your i/4?
  6. Oct 22, 2009 #5
    my mistake

    my mistake should be here:

    http://www.pixie.be/wrong.jpg [Broken]

    But I can't see it ...
    Could some one please help ? :(
    Last edited by a moderator: May 4, 2017
  7. Oct 22, 2009 #6


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    In going from the second contour to the third you seem to have just moved an i from the denominator to the numerator. You are now off by a sign. 5z-2z^2-2=(-2)(z-2)(z-1/2). There's another sign and a factor of two you made disappear.
  8. Oct 22, 2009 #7
    ow yes, that was a typing error !

    Aha, got it;
    After studying a lot of math, it's mostly the problem that i forget to do the 'simple' things correct ;) haha
    Stupid mistake, but thank you so much !
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