Help evaluating triple integral over tetrahedron I have a triple integral of $\iiint xyz\,dx\,dy\,dz$  over the volume of a tetrahedron with vertices $(0,0,0)$, $(1,0,0)$, $(0,1,0)$, and $(0,0,1)$. 
Normally I would just have limits 0 to 1 but that does not seem to work. How do I solve a problem like this?

Using the facts that the projection of the solid in the xy-plane is the triangle with vertices (0,0), (0,1), and (1,0), and that the top of the solid is the plane $x+y+z=1$, we can set up the integral as
$\displaystyle\int_{T} f(x,y,z) \;dV =\int_{0}^{1}\int_{0}^{1-x}\int_{0}^{1-x-y} f(x,y,z) \;dz dy dx$. 
