So ... the volume integral doesn't go to zero because the limiting process is different in spherical coordinates as opposed to Cartesian, and it matters whether I'm using a volume integral like ##\iiint dx~dy~dz## as opposed to ##\iiint dr~d\theta~d\phi## ?
EDIT: That is, I understand that the...
Homework Statement
Integrate $$\int_V \delta^3(\vec r)~ d\tau$$ over all of space by using V as a sphere of radius r centered at the origin, by having r go to infinity.
Homework EquationsThe Attempt at a Solution
This integral actually came up in a homework problem for my E&M class and I'm...