Calculating Volume of Tetrahedron Using Triple Integral: Step by Step Guide

[reddawg]

Homework Statement

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).

Homework Equations

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. . .

 

[reddawg]

Nevermind, I figured it out. I had to find the equation of the slanted plane by taking the cross product of two points getting the normal.

Problem solved.