Solving a triple integral with modulus I really can't figure out how to solve this triple integral
$$
\iiint_D|z|dxdydz
$$
on the domain $D$, that is so defined
$$
D = \left\{(x,y,z)\in\mathbb{R}^3: x^2+y^2-16 \leq z \leq 4 - \sqrt{x^2+y^2}\right\}
$$ 
Any ideas or solutions? Thanks in advance.

By changing the coordinates to cylindrical ones with a diffeomorphism  $\Psi $, 
$$
\Psi^{-1}(D)=\{(\rho,\theta,z): \rho ^2-16\leq z\leq 4-\rho\} = $$
$$
\{(\rho,\theta,z)\in \mathbb R_+ \times(0,2\pi)\times \mathbb R|\rho \in [-5,4], \
 z \in [\rho ^2-16,4-\rho] \}. 
$$
$D$ is measurable and so is $\Psi^{-1}(D) $. So by changing coordinates and Fubini's theorem you have:
$$
\int_D |z| dx dy dz =\iiint_{\Psi^{-1}(D)} |z|\rho d\rho d\theta dz=$$
$$=\int_0^{2\pi} \int_{-5}^4 \int _{\rho ^2-16}^{4-\rho} |z|\rho dz d\rho d\theta=$$
$$=2\pi \int_{-5}^4 \rho\int _{\rho ^2-16}^{4-\rho} |z| dz d\rho.$$
