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Dirac in a double integral

  1. Nov 16, 2008 #1

    I have a question about using the dirac function in a double integral.

    Lets say you have the double integral over the two values x1 and x2:

    int( int( sin(x1) * dirac(x1-x2) * sin(x2) ))

    Does this just simplify to a single integral:

    int( (sin(x1))^2 )

  2. jcsd
  3. Nov 17, 2008 #2


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    Staff Emeritus
    Science Advisor

    Well, that depends. You did not write any limits of integration.
    [tex]\int_a^b \delta(x- x1)f(x)dx[/tex]
    is equal to f(x1) IF [itex]a\le x1\le b[/itex] and 0 otherwise.
  4. Nov 17, 2008 #3
    The limits would be from -inf to inf. Thanks.
  5. Nov 18, 2008 #4
    AFAIK the answer is yes. But of course that non converging integral might produce some surprises.
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