Let $E$ be the solid region defined by the inequalities
$x \ge 0$,
$0\le z \le \sqrt(x^2 + y^2)$,
$x^2 + y^2 + z^2 \le 4$
Suppose that $E$ has mass density $\mu(x,y,z) = xz$. Calculate the total mass of $E$.
I know how to set up the problem and how to do it, I get confused on determining the bounds. For example we can find:
$0 \le z^2 \le x^2 + y^2$ and then when $z=0$, we get the circle $x^2 + y^2 \le 4$.
I am confused how to find the bounds of the triple integral with this information.