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Integration with Complex Numbers

  1. Nov 1, 2012 #1
    1. The problem statement, all variables and given/known data

    Evaluate ∫[itex]^{∏}_{0}[/itex]e(1+i)xdx

    2. Relevant equations

    I know that the Real part of this is -(1+e)/2 and the Imaginary part is (1+e)/2, but I can't get the right solution.

    I tried using u-substitution to create something that looked like ∫[itex]^{∏}_{0}[/itex]((eu)/(1+i))du

    but I don't think that's correct. How do I solve this? Thanks!
     
  2. jcsd
  3. Nov 1, 2012 #2

    Dick

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    Your substitution is fine. Except the u limits aren't the same as the x limits. Just do the u integration and then change back to x.
     
  4. Nov 1, 2012 #3

    HallsofIvy

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    Or, equivalently, change the limits of integration as you change the variable. You made the substitution u= (1+ i)x so that du= (1+ i)dx so that dx= du/(1+ i). If [itex]x= \pi[/itex] then [itex]u= (1+ i)\pi[/itex] and if x= 0, u= 0 so the integral becomes
    [tex]\frac{1}{1+ i}\int_0^{(1+i)\pi} e^udu[/tex]
     
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