- #1
gimak
- 56
- 1
Homework Statement
Prove the following
'()( − ) = −′()
∫-∞∞δ'(x)*f(x-a) = -f'(a)
Homework Equations
∫-∞∞δ'(x-a)*f(x) = f(a)
The Attempt at a Solution
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∫-∞ ∞δ'(x)*f(x-a) = ∫δ(x)*f(x-a)dx-∫f'(x-a)*δ(x)dx = f(-a) - f'(-a)
Went from 1st to second by integration by parts
Used integral definition of delta function to go to 3rd part