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Math Help - Triple Integrals

  1. #1
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    Feb 2010
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    Triple Integrals

    Here is my question

    Evaluate the triple integral where is bounded by the parabolic cylinder and the planes and .

    I set up dV to be dzdydx and the bounds to be {z,0,16-y^2}, I am confused on what to do for y, and {x,-4,4}. I tried {y,-4,4} because that is where the function crosses the z=0 plane, but when I evaluated it, it ended up to be incorrect. Any help would be greatly appreciated.
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  2. #2
    Super Member
    Joined
    Aug 2008
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    Try and learn how to draw them in Mathematica then put it into the form:

    \int_{x=a}^{x=b}\int_{y=f(x)}^{y=g(x)}\int_{z=f_1(  x,y)}^{z=f_2(x,y)} u(x,y,z)dzdydx

    So z goes from the x-y plane up to the function f(x,y)=16-y^2, y goes from the two "function" of x, y=-4 and y=4 and then x goes from the range of -4 to 4:

    \int_{-4}^{4}\int_{-4}^{4}\int_{0}^{4-y^2} x^2 e^y dzdzdx
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