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Math Help - Triple Integral Problem

  1. #1
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    Triple Integral Problem

    Hello,
    I have been working on this problem for a while and I have tried about 5 or six different ways and can't get the answer.
    If you could help that would be awesome.

    Find triple integral ZZZT x dV, where T is the tetrahedron bounded by the planes x=1, y=1, z=1 and x+y+z=2. I can't seem to get the boundaries right.

    For my latest attempt I tried:

    2-y-x < z < 1
    1-x < y < 1
    0 < x < 1

    I was trying to find the missing piece (like the corner of the square) then multiply the answer by three to get the part of the tetrahedron within the boundary but I got 1/4 and the answer is 1/8.
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  2. #2
    Junior Member
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    Re: Triple Integral Problem

    Never mind. I figured out the answer. I used the same technique as above but I changed my y boundary to 1-x < y < 0 however when I look back I still don't understand how that is. Can anyone help me understand this part.
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  3. #3
    Junior Member
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    Re: Triple Integral Problem

    Never mind again. I figured it out.
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