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Average of function (using dirac delta function)

  1. Jan 13, 2016 #1
    1. The problem statement, all variables and given/known data
    Compute the average value of the function:

    f(x) = δ(x-1)*16x2sin(πx/2)*eiπx/(1+x)(2-x)

    over the interval x ∈ [0, 8]. Note that δ(x) is the Dirac δ-function, and exp(iπ) = −1.

    2. Relevant equations
    ∫ dx δ(x-y) f(x) = f(y)

    3. The attempt at a solution
    Average of f(x) = 1/8 ∫from 0 to 8 δ(x-1) dx 16x2sin(πx/2)*(-1)/(1+x)(2-x)
    Average of f(x) = -1

    Is this correct? I'm unsure of whether you can just use δ(x-a) = δ(x-1) and let a=1 and not let a=-1? I don't get how to use this bit of the function as I seem to have just ignored the negative sign.

    Many thanks.
     
  2. jcsd
  3. Jan 13, 2016 #2
    From the problem statement, your a is = to 1 not -1.
     
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