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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

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 ρ(x,y,z) .

The mass of the solid is, m=liml,m,ni=1lj=1mk=1nρ(

(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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Chapter 15 Solutions

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