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2 variable delta function integration

  1. Aug 19, 2007 #1

    Gin

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

    [tex]\int^{A}_{-A}[/tex][tex]\int^{Bx}_{-Bx}c\delta(xcos\varphi+ysin\varphi-d)dydx[/tex]
    where A, B, c, d are constant
    2. Relevant equations



    3. The attempt at a solution
    I have tried a few different ways to integrate this, but am completely confused with what happens to this kind of delta function when you integrate it. I know integrating a delta function usually gives you 1 but I don't think this can work in this case. The answer has A,B,c and d in it, so the limits must be used somewhere. This is one step in a much longer problem, but it is frustrating to get close to the end and get stuck because I can't find anything anywhere about delta functions of 2 variables. Some help would really be appreciated.
     
  2. jcsd
  3. Sep 16, 2011 #2
    Did you or anyone else figure out how to deal with this? I have the same problem.
     
  4. Sep 16, 2011 #3

    Mute

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    Homework Helper

    One could, for example, use the following property of a delta function:

    [tex]\delta(af(x)) = \frac{1}{|a|}\delta(f(x))[/tex]

    to factor out the cosine in the argument of the delta function and then perform the x integration. The x integration is then easy, but there's a trick - you don't know for sure if the delta function argument is zero inside the limits of x integration, so you'll have to think carefully about that.
     
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