1. The problem statement, all variables and given/known data Essentially, do the volume integral of z^2 over the tetrahedron with vetices at (0,0,0) (1,0,0) (0,1,0) (0,0,1) 3. The attempt at a solution There seems to be a ton(!) of brute-force algebra involved. Enough to make me question if I'm doing the problem right. I set up the triple integral of z^2 in the order dzdydx with the following limits of integration. z=0 to z= 1-x-y y=0 to y= 1-x x=0 to x=1 It didn't take to long for me to end up with trying to integrate a humongous polynomial in the second interval. Evaluating z^3 / 3 at z = 1-x-y was fun enough. But now after integrating again, I have to evaluate y/3 -xy-y^2/2+xy^2+x^2*y + y^3/3 + 1/3*x^3*y et cetera at y = 1-x seems to be a nightmare. Am I tackling this the wrong way?