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Math Help - Triple integral with cylindrical coordinates

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    Triple integral with cylindrical coordinates

    I need to evaluate the triple integral over the region W of:

    f(x,y,z) = x^2 + y^2 + z^2 where W is the region r greater than or = to 0 and less than or = to 4, theta greater than or = tp pi/4 and less than or = to 3pi/4, z greater than or = to -1 and less than or less than 1

    using those limits I integrated (r^2 + z^2) r dr dtheta dz is this correct?
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    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Frostking View Post
    I need to evaluate the triple integral over the region W of:

    f(x,y,z) = x^2 + y^2 + z^2 where W is the region r greater than or = to 0 and less than or = to 4, theta greater than or = tp pi/4 and less than or = to 3pi/4, z greater than or = to -1 and less than or less than 1

    using those limits I integrated (r^2 + z^2) r dr dtheta dz is this correct?
    Yes. The integral you're integrating should be \int_{-1}^1\int_{\frac{\pi}{4}}^{\frac{3\pi}{4}}\int_0^4 \left(r^3+z^2r\right)\,dr\,d\theta\,dz
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