Chapter 15, Problem 4RCC

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

If a lamina occupies a plane region *D* and has density function *ρ*(*x*, *y*), write expressions for each of the following in terms of double integrals.

(a) The mass

(b) The moments about the axes

(c) The center of mass

(d) The moments of inertia about the axes and the origin

(a)

To determine

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

Explanation

**Given:**

A lamina has the density function over the region *D* is

The mass of the lamina is,

(b)

To determine

**To write:** The expression for the moments about the axis.

(c)

To determine

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

(d)

To determine

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

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