# Homework Help: Integrating the Dirac Delta function

1. Jan 30, 2013

### Bugeye

1. The problem statement, all variables and given/known data
I am trying to integrate the function
$\int _{-\infty }^{\infty }(t-1)\delta\left[\frac{2}{3}t-\frac{3}{2}\right]dt$

2. Relevant equations

3. The attempt at a solution
I think the answer should be $\frac{5}{4}$ because $\frac{2}{3}t-\frac{3}{2}=0$ when t=9/4. then (9/4-1) = 5/4. However, when I put the equation into Mathematica, it gives me an anser of 15/8.

2. Jan 30, 2013

### Dick

There's more to it than that. Do a change of variables u=2t/3-3/2. Don't forget du isn't the same as dt.

3. Jan 30, 2013

### Ray Vickson

You need to be really, really careful when dealing with things like δ(f(t)). In your case, just change variables to x = (2/3)t.

4. Jan 30, 2013

### Bugeye

Great, I got it, thanks a lot.