# Problem with integrals

1. Oct 1, 2013

### cyc454

Hi! I've got a problem with an integral. Let's assume we've got something like this:

R3d3x1R3d3x2R3d3x3R3d3x4P(|x1|)P(|x3|)δ(x1+x2)δ(x3+x4)W(|x1+x2|)W(|x3+x4|)

xi is a vector
The "δ" is the Dirac delta.
P(|x|i) & W(|xi+xj|) are some functions
I would like to make it looks a bit simpler---I mean get rid of deltas and two integrals. How can I make it?
Thanks for help and sorry for spelling mistakes!
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Oct 1, 2013

### Bryson

What have you attempted? Do you understand the properties of the delta function?

3. Oct 2, 2013

### cyc454

if the xi=-xj then δ ≠0.

R3δ(x)d3x should be equal 1. Well, actually it should looks

like this:

-∞δ(x)dx=1

but it is the same I thing.. This is all I know.

4. Oct 2, 2013

### Bryson

Okay, also note that $\int \cdots \int f(\vec{x}) \delta(\vec{x} - \vec{x}_o) d^Nx = f(\vec{x}_o)$. This can allow you to fix some variables.

My next question is, are we integrating from $-\infty \rightarrow \infty$? If the variable being integrated is not within the bounds, we can simplify things greatly.

I must say, it has been awhile since I have done integrals of this form.

5. Oct 2, 2013

### cyc454

Well, we are integrating it over the entire R3..
I don't get it. There isn't any function depending on x. there is only P and W that depend on |x| or |xi+xj|

PS I can't put P and W before the integrals, can I?
PPS One more thing. There is a integral:
∫d3x1
and let's assume x1=x2+x3 so the d3x1=d3x2+d3x3. So after substitution
∫d3x1=∫d3x2+∫d3x3? is it correct?

Last edited: Oct 2, 2013