Volume of tetrahedron

1. The problem statement, all variables and given/known data

Set up an integral to find the volume of the tetrahedron with vertices

(0,0,0), (2,1,0), (0,2,0), (0,0,3).





2. Relevant equations







3. The attempt at a solution

My method of solving this involves using a triple integral. The first step is deciding on the bounds of the triple integral. If you can envision the tetrahedron in the x, y, z plane:



The base of the tetrahedron has equations: y = x/2 and y = (4-x)/2



I know the bounds for x and y:



x goes from 0 to 2

y goes from (x/2) to (4-x)/2



How do I find the bounds for z? I need an equation relating z to x and y. . .