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Math Help - help me with triple integral

  1. #1
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    help me with triple integral

    \int \int_{E} \int x^2e^y dV

    E is bounded by parabolic cylinder z = 1-y^2 and the plane z=0, x=1 and x=-1
    so the boundary should be:

     0 \leq z \leq 1-y^2

    -1 \leq y \leq 1

    -1 \leq x \leq 1

    are they right?
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  2. #2
    Super Member redsoxfan325's Avatar
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    Looks good.
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  3. #3
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    but if i integrate this: \int^1_{-1} \int^1_{-1} \int^{1-y^2}_0 x^2e^y dz dy dx, I got zero eventually which is not possible.

    What is wrong?
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  4. #4
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by zpwnchen View Post
    but if i integrate this: \int^1_{-1} \int^1_{-1} \int^{1-y^2}_0 x^2e^y\,dz\,dy\,dx, I got zero eventually which is not possible.

    What is wrong?
    I just evaluated it on my TI-89 and got

    -\frac{2(e^2-5)}{3e}
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