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Evaluating this particular integral

  1. Nov 27, 2014 #1
    I'm trying to numerically evaluate an integral in a paper of the form;

    ∫ ƒ(Ψ) dΨ ∫ ƒ(X,Ψ) dX

    The second part of the integral contains a function of both X and Ψ, yet it only needs to be integrated with respect to X. This has confused me on what to use as a value for Ψ.

    I've attached the integral below (excuse the scribbling). As you can see, the last integral is evaluated for dX, but contains Ψ and X.

    Any help much appreciated.

    WP_20141127_20_17_31_Pro.jpg
     
  2. jcsd
  3. Nov 27, 2014 #2
    Have you thought about treating ##\psi## as a constant in the second integral? It doesn't appear to me that the second integral has a function of both ##\chi## and ##\psi##.
    Just a thought.
     
  4. Nov 27, 2014 #3
    I did think about that but in the context ##\psi## and ##\chi## are analogous to y and x coordinate system so it's like a integral over 2D space. If I chose ##\psi## as a constant... I wouldn't know what to set it as. Also, ##\alpha## is a function of ##\psi## making the second integral a function of both ##\psi## and ##\chi##.
     
  5. Nov 27, 2014 #4
    I see what you mean. Honestly, the way I would do it is evaluate it with respect to ##\chi## but treat ##\psi## as a constant. You don't really need to worry about "what to set ##\psi## as". When you integrate a function of ##\psi## with respect to ##\chi##, you'll still get a function of ##\chi## as a result, so setting ##\psi## equal to something for the sake of doing the integral isn't much of a concern.
     
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