Chapter 15, Problem 8RCC

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Suppose a solid object occupies the region *E* and has density function *ρ*(*x*, *y, z).* Write expressions for each of the following.

(a) The mass

(b) The moments about the coordinate planes

(c) The coordinates of the center of mass

(d) The moments of inertia about the axes

(a)

To determine

**To write:** The expression for the mass.

Explanation

**Given:**

A solid has the density function over the region *E* is denoted by

The mass of the solid is,

(b)

To determine

**To write:** The expression for the moments about the coordinate planes.

(c)

To determine

**To write:** The expression for the coordinates of the center of mass.

(d)

To determine

**To write:** The expression for the moment of inertia about the axes.

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