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I Complex integral of a real integrand

  1. May 5, 2017 #1
    I am trying to do the following integral:

    $$\int_{\pi f}^{3\pi f} dx \sqrt{\cos(x/f)}.$$

    Wolfram alpha - http://www.wolframalpha.com/input/?i=integrate+(cos(x))^(1/2)+dx+from+x=pi+to+3pi gives me

    $$\int_{\pi f}^{3\pi f} dx \sqrt{\cos(x/f)} = 4f E(2) = 2.39628f + 2.39628if,$$

    where E is the elliptic function.

    Mathematica also gives me the same answer. How can the integral of a real integrand with real limits be complex?
     
  2. jcsd
  3. May 5, 2017 #2

    Orodruin

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    It cannot. Your integrand is not real.
     
  4. May 5, 2017 #3
    got it!
     
  5. May 5, 2017 #4

    Mark44

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    What's the meaning of 'f' in the limits of integration and in cos(x/f)? You don't have it in your Wolframalpha link. When I click the WA link you provided, it says that it doesn't understand the query, and gives a result of 1/2.
     
  6. May 5, 2017 #5

    Orodruin

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    Remove the backslash ...
     
  7. May 5, 2017 #6
    This question is with regards to tunneling in false vacuum decay.
    ##f## is a constant. Here is the link that works:

    http://www.wolframalpha.com/input/?i=integrate+(cos(x))^(1/2)+dx+from+x=pi+to+3pi
     
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