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 ZZZ_{T}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.