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Math Help - Triple Integral

  1. #1
    Junior Member
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    Nov 2007
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    58

    Triple Integral

    I am having trouble with the following triple integral:

    Triple Integral (over E), where E is bounded by the cylinder (y^2) + (z^2) = 9, and the planes x = 0, y = 3x, and z = 0. The density function of the triple integral is defined as f(x, y, z) = z dV.

    The biggest problem I am having is defining the boundaries for each integral (i.e. iterating the integral).

    Thanks for any help.
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  2. #2
    Newbie
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    Mar 2009
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    La Jolla, CA
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    So I made a picture of the graph and came up with the domain lying in the xy plane. It was bounded by x = 0 and y=3x and y = 3.

    y=3 comes from when z = 0 in the xy plane, y^2 = 9, y = 3

    So it forms a triangle. It is vertically linear, so y ranges from 0 to 3, x ranges from 0 to y/3. Then finally z ranges from 0 to sq(9-y^2)

    Then all you have to do is integrate.
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