Question: A solid $E$ is enclosed by the planes $z = 0, z = x + y + 5$ and by the cylinders $x^2 + y^2 = 4, x^2 + y^2 = 9$. The density at any point is equal to its distance from the $yz$-plane. Find the mass of $E$.
Work: So far I've converted the problem into cylindrical coordinates
$$\int_0^{2\pi} \int_2^3 \int_0^{r(sin\theta+cos\theta) + 5} r \,dz\,dr \,d\theta$$
Evaluating this in mathematica gave me $25 \pi$; , which was not correct. I then thought that the question was stating the radius from the axis of the cylinder determined the mass so I tried using $r^2$ in place of $r$ and got $190\pi/3$, and that was not correct. I'm very confused on how to tackle this problem. Thank you for any help.
Guide:
The density is equal to its distance from the $yz$-plane, hence you are suppose to integrate $|x|=r|\cos\theta|$ rather than integrating over $1$.
\begin{align}\int_0^{2\pi} \int_2^3 \int_0^{r(sin\theta+cos\theta) + 5} r^2 |\cos(\theta)| \,dz\,dr \,d\theta \end{align}