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2 variable delta function integration

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Gin
#1
Aug19-07, 09:12 PM
P: 3
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.
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Judithku
#2
Sep16-11, 03:35 AM
P: 4
Did you or anyone else figure out how to deal with this? I have the same problem.
Mute
#3
Sep16-11, 07:58 AM
HW Helper
P: 1,391
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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