# Thread: Total Mass Integration Question

1. ## Total Mass Integration Question

Find the total mass of a mass distribution of density σ in a region T in space.

$\displaystyle \sigma = 1 + y + z^2$, T the cylinder $\displaystyle y^2 + z^2 \leq\ 9, 1\leq x\leq 13$

$\displaystyle \int\int\int _{T}\sigma dxdydz$

I'm pretty sure I know how to integrate it but I am not sure how to get the upper and lower limits for dy and dz

2. Have you learned cylindrical coordinates yet? If so, then we may set

\displaystyle \begin{aligned} x&=x\\ y&=r\cos\theta\\ z&=r\sin\theta \end{aligned}

to obtain the integral

$\displaystyle \int_0^{2\pi}\int_0^3\int_1^{13}(1+r\cos\theta+r^2 \sin^2\theta)\,r\,dx\,dr\,d\theta.$