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Integral of delta function multiplied by a Heaviside step function

  1. Mar 1, 2013 #1
    1. The problem statement, all variables and given/known data
    consider two functions:ψ(x) which is eqaul to zero at a,that is ψ(a)=0
    and f(x)=H(x-a)*β(x)+(1-H(x-a))*γ(x)
    where H(x-a) is the heaviside step function and β(x),γ(x) is the continous function.
    it seems that the derivative of f(x) is not exist.
    the question is whether ∫δ'(x-a)*ψ(x)*f(x)dx make sense?
    δ'(x-a) is the derivative of the delta function.
    if the above integral make sense,how to get the value of it?
    Any hints will be grateful.:shy:
     
    Last edited: Mar 1, 2013
  2. jcsd
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