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Math Help - Total Mass Integration Question

  1. #1
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    Total Mass Integration Question

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

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

    \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
    Last edited by sazafraz; November 4th 2009 at 10:05 AM.
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  2. #2
    Senior Member
    Joined
    Dec 2008
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    Have you learned cylindrical coordinates yet? If so, then we may set

    \begin{aligned}<br />
x&=x\\<br />
y&=r\cos\theta\\<br />
z&=r\sin\theta<br />
\end{aligned}

    to obtain the integral

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