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Math Help - Triple integrals

  1. #1
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    Triple integrals

    f(x, y, z) = x^2 ; G is tetrahedron bounded by the coordinate planes and the plane octant with equation x + y + z = 1

    ∫ ∫ ∫ x^2 dzdydx

    I try to set up the ranges for x, y and z..

    x+y+z = 1
    z = 1-x-y......set the limits for z from z=0 to z = 1-x-y

    x+y+z = 1
    if, z = 0, y = 1-x ........set the limits for y = 0 to y = 1-x

    x+y+z = 1
    if, z = 0 , y = 0 ........x = a set the limits from x = 0 to x =1

    first.. i need help to confirm that my ranges are correct..
    because.. i've done the integration and got the wrong answer..
    i've double checked my integration and it is right..
    there must be something wrong with my ranges.. i guess...
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  2. #2
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    Re: Triple integrals

    Quote Originally Posted by nameck View Post
    f(x, y, z) = x^2 ; G is tetrahedron bounded by the coordinate planes and the plane octant with equation x + y + z = 1

    ∫ ∫ ∫ x^2 dzdydx

    I try to set up the ranges for x, y and z..

    x+y+z = 1
    z = 1-x-y......set the limits for z from z=0 to z = 1-x-y

    x+y+z = 1
    if, z = 0, y = 1-x ........set the limits for y = 0 to y = 1-x

    x+y+z = 1
    if, z = 0 , y = 0 ........x = a set the limits from x = 0 to x =1

    first.. i need help to confirm that my ranges are correct..
    because.. i've done the integration and got the wrong answer..
    i've double checked my integration and it is right..
    there must be something wrong with my ranges.. i guess...
    Have you tried doing a sketch of your region in 3D and a sketch of the required region in the x-y plane?
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  3. #3
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    Jul 2011
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    Re: Triple integrals

    As stated in the post above, you should always draw the picture in 3d and in the x-y plane (or which ever one you feel confortable in)

    Here is the picture, I hope this help you.

    Picture: http://img820.imageshack.us/img820/6339/helpdj.png

    edit: sorry it was solved, didn't read carefully!
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