Chapter 14.6, Problem 65E

Average Value In Exercises 63-66, find the average value of the function over the given solid region. The average value of a continuous function f(x, y, z) over a solid region Q is $\text{Average}\text{value}=\frac{1}{V}{\displaystyle \underset{Q}{\iiint }f(x,y,z)dV}$

where V is the volume of the solid region Q.

$f(x,y,z)=x+y+z$ over the tetrahedron in the first octant with vertices (0, 0, 0), (0, 2, 0) and (0, 0, 2)