Question

Use triple integrals to calculate the average value of F(x,y,z) over the given region: F(x,y,z) =...

Use triple integrals to calculate the average value of F(x,y,z) over the given region:

F(x,y,z) = xyz

on the cube in the first octant delimited by the coordinate planes and the planes

x = 1, y = 1, z = 1

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Answer #1

If f(x,y,z) is integrable over a bounded region, then the average value of the function is given by the triple integral of the function over the volume divided by the volume covered by the region.

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