# Homework Help: Integral of delta function multiplied by a Heaviside step function

1. Mar 1, 2013

### jht529100

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