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Math Help - Triple Integral

  1. #1
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    Triple Integral

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

    Thanks.
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  2. #2
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    Apr 2009
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    Tuscaloosa, Alabama
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    Make a graph of x vs y and x vs z.

    The points of intersection on the x vs y graph are where 8x^2=16x (x=0,2)
    So, for the x integral let x go from 0 to 2.

    Now for the y integral..
    On the x interval [0,2] y=8x^2 < y=16x so let y range from 8x^2 to 16x.

    Now for the z integral..
    It is bounded by z=0 and z=4x so let z range from 0 to 4x.

    dV=dz dy dx

    Now just integrate the function with respect to z, and then plug in the limiting values.
    Integrate with respect to y and plug in the limiting values. Finally, integrate with respect to x from 0 to 2.

    Hope that helps..
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