Chapter 15.6, Problem 53E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

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

To determine

**To find:** The average value of the function
*L*

Explanation

**Given:**

The average value of the function is,

Where
*E* and the function
*L* lies in the first octant and vertex at the origin and the edges are parallel to the coordinate axes.

**Calculation:**

**Formula used:**

If
*z* the,

The region

*E*, Therefore

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