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The average value of a function f(x, y, z) over a solid region E is defined...

The average value of a function f(x, y, z) over a solid region E is defined to be fave = 1 V(E) E f(x, y, z) dV where V(E) is the volume of E. For instance, if ρ is a density function, then ρave is the average density of E. Find the average value of the function f(x, y, z) = 5x2z + 5y2z over the region enclosed by the paraboloid z = 4 − x2 − y2 and the plane z = 0.

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