# Dirac Delta Integral

1. Aug 30, 2011

### iamalexalright

1. The problem statement, all variables and given/known data
For some reason these are just messing me up. I need to prove:

1. $\delta(y)=\delta(-y)$

2.$\delta^{'}(y) = -\delta^{'}(-y)$

3.$\delta(ay) = (1/a)\delta(y)$

In 2, those are supposed to be first derivatives of the delta functions

2. Relevant equations
Use an integral with a test function

3. The attempt at a solution
Need a small hint

2. Aug 30, 2011

### Dick

You need to prove the integral of delta(y)*f(y)*dy (what is that?) is equal to the integral of delta(-y)*f(y)*dy where y goes from -infinity to infinity and f is a test function. Try a change of variable u=(-y) and use the properties of the delta function. Don't forget to pay attention to what happens to the limits of integration when you change the variable.