1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    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

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    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

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    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 !
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook