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Math Help - triple integral

  1. #1
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    Question triple integral

    i'm new to triple integrals and having trouble setting this problem up.
    its the equation f(x,y,z)= xy
    bound by the planes x=0, y=0, z=0, x+2y+4z=8
    how do i find the boundaries for integration?
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  2. #2
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    Find out where the plane intersects the y and x-axis. You can do that from the equation x+2y+4z=8 first let x=0 and z=0 so then 2y=8, then let z=0 and y=0 so then x=8 then you can find x_a and f(x) below and set up:

    \int_0^{x_a}\int_0^{f(x)} \int_0^{g(x,y)} dzdydx

    or:

    \int_0^{x_a}\int_0^{f(x)} 1/4(8-x-2y) dydx
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  3. #3
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    thanks so x is from 0 to 8, y from 0 to 4, and z from 0 to 2?
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  4. #4
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    Quote Originally Posted by holly123 View Post
    thanks so x is from 0 to 8, y from 0 to 4, and z from 0 to 2?
    No. y goes from the x-axis to where the plane x+2y+4z=8 cuts through the x-y plane right? Isn't that just y=1/2(8-x)? And z goes from the x-y plane up to the surface x+2y+4z=8 solved for z. Wouldn't that then be:

    \int_0^8 \int_0^{1/2(8-x)} \int_0^{1/4(8-x+2y)} dz dy dx

    or it's just a double integral:

    \int_0^8 \int_0^{1/2(8-x)}1/4(8-x+2y) dy dx
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  5. #5
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    ughhh i set it up this way, as well as many variations of this way, and am getting a completely wrong answer. i have worked on this problem for hours and done it several times. the answer in the back of the book is 256/15
    i have gotten 2816/3 and 15104/15 many times. how in the world do you do this problem?!?
    Last edited by holly123; November 1st 2009 at 06:22 PM.
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