# d^3x in integration?

#### blorpinbloo

So I'm working on a research project for my physics professor and although I'm a physics and math major, he's giving me a few problems with mathematical concepts that's beyond what I've taken so far. Here is the latest integral he is having me solve:

$$\displaystyle \[ \int \frac{\sin \left(kr-atan \left(ka \right)\right)}{kr} \frac{\sin \left(k'r-atan \left(k'a \right)\right)}{k'r} {d^3r}$$

I haven't solved integrals that have looked like that with the d^3r term. What do you refer to this concept as (so I can know what to look for in order to study it)? And does anyone happen to have any resources where I can read up on solving them?

#### Ackbeet

MHF Hall of Honor
It's the volume element in 3 dimensions, equivalent to dx dy dz, or whatever the volume element is in whatever coordinate system you're in (spherical, cylindrical, etc.). It's a Calc III topic. Here $$\displaystyle r=\sqrt{x^{2}+y^{2}+z^{2}}.$$

• HallsofIvy and blorpinbloo

#### blorpinbloo

Ohhh, I see. I guess I just haven't seen the notation in a while and forgot about it. Thanks

#### Ackbeet

MHF Hall of Honor
You're very welcome.