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Math Help - Triple Integral Problem

  1. #1
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    Triple Integral Problem

    So I'm having a little trouble with a triple integral problem. I haven't done many of these, so I'm not sure if my bounds of integration are correct etc. Anyway, here is the problem as stated:

    "f(x,y,z) = z

    W is the region bounded by z=0, x^2 +4y^2=4 and z=x+2

    Integrate f over the region W."

    I've attached my attempt at solving this. Basically I'm stuck at evaluating the last iterated integral, which makes me think I've done something wrong before getting there...

    Would appreciate any help!
    Attached Thumbnails Attached Thumbnails Triple Integral Problem-img469.jpg  
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Triple Integral Problem

    Quote Originally Posted by gralla55 View Post
    "f(x,y,z) = z W is the region bounded by z=0, x^2 +4y^2=4 and z=x+2 Integrate f over the region W."
    Hint Using the transformation (x,y,z)=(x,2v,z) and cylindric coordinates you'll obtain the region

    \begin{Bmatrix}0\leq \theta \leq 2\pi \\0\leq \rho \leq 2\\0\leq z \leq 2+\rho \cos\theta\end{matrix}
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