Question: The average value of a function f (x, y, z) over a solid region E is defined to be where V(E) is the volume of

The average value of a function f (x, y, z) over a solid region E is defined to be 1 fave V(E) J] F(x, y, z) dV where V(E) is the volume of E. For instance, if p is a density function, then p_ave is the average density of E.

Find the average value of the function f (x, y, z) = xyz over the cube with side length L that lies in the first octant with one vertex at the origin and edges parallel to the coordinate axes.

1 fave V(E) J] F(x, y, z) dV

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