I am having trouble with the following question:
Find the mass of a ball B given by (x^2) + (y^2) + (z^2) <= (a^2) if the density at any point is proportional to its distance from the z-axis.
Any ideas or help would be appreciated. Thanks!
You need to change variables. Rectangular is painful. The density here is
$\displaystyle kr=k\sqrt{x^2+y^2}=k\rho\sin\phi$, but the k's cancel, so you can let k=1.
Try spherical, where the Jacobian is $\displaystyle \rho^2\sin\phi$.
If you're integating over the entire ball, then $\displaystyle 0<\rho <a$, $\displaystyle 0<\theta <2\pi$ and $\displaystyle 0<\phi<\pi$.