d^3x in integration?

Jan 2010
11
0
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
Jun 2010
6,318
2,433
CT, USA
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 \(\displaystyle r=\sqrt{x^{2}+y^{2}+z^{2}}.\)
 
Jan 2010
11
0
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
Jun 2010
6,318
2,433
CT, USA
You're very welcome.