Chapter 14.5, Problem 37ES

Let G be the tetrahedron in the first octant bounded by the coordinate planes and the plane

$\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1\left(a>0,b>0,c>0\right)$

(a) List six different iterated integrals that represent the volume of G.

(b) Evaluate any one of the six to show that the volume of G is $\frac{1}{6}abc.$