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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

Set up, but do not evaluate, integral expressions for (a) the mass, (b) the center of mass, and (c) the moment of inertia about the z-axis.

47. The solid of Exercise 21;  ρ ( x , y , z ) = x 2 + y 2

21. The solid enclosed by the cylinder y = x2 and the planes z = 0 and y + z = 1

(a)

To determine

To find: The integral expression for the mass and not to evaluate the value.

Explanation

Given:

From exercise 21 notice that, the solid enclose by the cylinder y=x2 and the planes z=0 , y+z=1 and the density is given by ρ(x,y,z)=x2+y2 .

Calculation:

Mass of the solid, mass(m)=density×volume . Here the density is given by ρ(x,y,z)=x2+y2 .

The mass of the solid is, m=liml,m,ni=1lj=1mk=1nρ(xij*,yij*,zij*)ΔA=Eρ(x,y,z)dA

(b)

To determine

To find: The integral expression for the center of mass and not to evaluate the value.

(c)

To determine

To find: The integral expression for the moment of inertia about the z-axis and not to evaluate the value.

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Chapter 15 Solutions

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