I'm having trouble on a homework question evaluating $\int\int\int_D dxdydz$, where $D$ is the solid ball centered at $(1,2,3)$ with radius 4.
The professor suggested converting to spherical coordinates, but I guess that's what's throwing me off a bit. Based on my notes I know $x=\rho\sin(\phi)\cos(\theta)$, $y=\rho\sin(\phi)\sin(\theta)$, and $z=\rho\cos(\phi)$.
I think my limits of integration will be $\int_0^\pi\int_0^{2\pi}\int_0^4$...$d\rho d\theta d\phi$, but I'm not sure what my integrand should be.
Any suggestions would be appreciated.