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Integrating the Dirac Delta function

  1. Jan 30, 2013 #1
    1. The problem statement, all variables and given/known data
    I am trying to integrate the function
    [itex]\int _{-\infty }^{\infty }(t-1)\delta\left[\frac{2}{3}t-\frac{3}{2}\right]dt[/itex]

    2. Relevant equations

    3. The attempt at a solution
    I think the answer should be [itex]\frac{5}{4}[/itex] because [itex]\frac{2}{3}t-\frac{3}{2}=0[/itex] when t=9/4. then (9/4-1) = 5/4. However, when I put the equation into Mathematica, it gives me an anser of 15/8.
     
  2. jcsd
  3. Jan 30, 2013 #2

    Dick

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    There's more to it than that. Do a change of variables u=2t/3-3/2. Don't forget du isn't the same as dt.
     
  4. Jan 30, 2013 #3

    Ray Vickson

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    You need to be really, really careful when dealing with things like δ(f(t)). In your case, just change variables to x = (2/3)t.
     
  5. Jan 30, 2013 #4
    Great, I got it, thanks a lot.
     
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