The average value of a function f ( x, y, z ) over a solid region E is defined to be f a v e = 1 V ( E ) ∭ E f ( x , y , z ) d V where V( E ) is the volume of E. For instance, if ρ is a density function, then ρ ave is the average density of E . 53 . 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.
The average value of a function f ( x, y, z ) over a solid region E is defined to be f a v e = 1 V ( E ) ∭ E f ( x , y , z ) d V where V( E ) is the volume of E. For instance, if ρ is a density function, then ρ ave is the average density of E . 53 . 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.
The average value of a function f (x, y, z) over a solid region E is defined to be
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where V(E) is the volume of E. For instance, if ρ is a density function, then ρave is the average density of E.
53. 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.
Evaluate
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Chapter 15 Solutions
Calculus: Early Transcendentals, Loose-leaf Version, 9th
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