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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

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BuyFindarrow_forward

Calculus: Early Transcendentals

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 ρ(x,y) .

The mass of the lamina is, m=limk,li=1kj=1lρ(x

(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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Chapter 15 Solutions

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