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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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Section
BuyFindarrow_forward

Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

Refer to the figure and find the volume generated by rotating the given region about the specified line.

Chapter 5.2, Problem 26E, Refer to the figure and find the volume generated by rotating the given region about the specified

2 about BC

To determine

To find:

The volume generated by rotating the region R2 about the line  BC by using the figure.

Explanation

1)  Concept:

i. If the cross section is a disc and the radius of the disc is in terms of x  or y, then the area A=π radius2

ii. The volume of  the solid revolution about the y-axis is

V= abA(y)dy

2) Given:

Figure:

3) Calculation:

Rotating R2 about BC that is about line y=1.

Rotating R2 about BC that is the line y=1, the cross section is perpendicular to the x-axis and it is a disc with the radius r=1-x4. Because it is the distance from the curve y= x4 to the axis of the rotation line BC (y=1)

The solid lies between x=0 and  x=1

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