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Solving simple dirac delta function

  1. Nov 12, 2007 #1
    1. The problem statement, all variables and given/known data
    [tex]\int[/tex] x[delta(x)-delta(x/3+4)] dx


    2. Relevant equations

    so I'm supposed to use this principle:
    [tex]\int[/tex] f(x)delta(x-xo)dx=f(xo)


    3. The attempt at a solution
    So it seems simple but I just want to make sure that I'm applying the above principle correctly.

    I separate the terms so the problem becomes:
    [tex]\int[/tex] x[delta(x)]dx - [tex]\int[/tex] x[delta(x/3+4)]dx

    Now the first term will go to zero because xo=0. The second term, I'm a little unsure. Should I transform the inside of the delta function so that delta(x/3+4) becomes delta(x+12)? Or should I transform the f(x) from x to x/3, then use that principle? Any suggestions are greatly appreciated.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 12, 2007 #2

    Galileo

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    Use a substitution and a test function to find out what delta(ax) is in terms of delta(x).
    It's a very useful relation to know in general and makes this problem easy once you got it.

    Hint: Split the cases a>0 and a<0.
     
  4. Nov 12, 2007 #3
    ok...here's what I found

    So delta(ax)=[delta(x)]/|a|. Then could I do the following:

    Given delta(x/3+4)=[delta(x+12)]/|3|. Basically, I factored out the 1/3, and so a=1/3.
     
  5. Nov 12, 2007 #4

    Galileo

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    Right, but then you get 3*delta(x), not delta(x)/3.
     
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