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Calculate complex integral as line integral

  1. Oct 11, 2013 #1
    1. The problem statement, all variables and given/known data
    We need to calculate this complex integral as line integral:
    mvw98gi92v0r12s9uk9w.png


    2. Relevant equations



    3. The attempt at a solution
    This is correct, I guess:
    v8yzkdwcftef6j9gch6p.png

    But not sure about this part:
    o09jbdaoynkhyxn1jg0x.png

    Are dx, dy, x, y chages correct or there is other method to use?
     
  2. jcsd
  3. Oct 11, 2013 #2
    Not hard to numerically integrate it and check your results right?

    Code (Text):

    NIntegrate[(z^2 + z*Conjugate[z])*I*Exp[I*t] /. z -> Exp[I*t], {t, Pi, 0}]
     
    but I just let [itex]z=e^{it}[/itex] to check that. What's wrong with just doing that symbolically from the start.
    So my suggestion is for you to compute the expression your derived, compute it numerically in Mathematica or other, and thirdly, by letting [itex]z=e^{it}[/itex] and computing it by evaluating the integral in t and then compare the three.
     
  4. Oct 22, 2013 #3
    Of course... thanks for idea. I cheked results and they were equal.
     
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