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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 19E, Refer to the figure and find the volume generated by rotating the given region about the specified

1 about OA

To determine

To find:

The volume generated by rotating the region R1 about theline  OA 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 x-axis is

V= abA(x)dx

2) Given:

Figure:

3) Calculation:

Here, the line OB appears to be the line y=x and line OA appears to be the line  y=0.

On rotating R1 about OA that is the line  y=0, the cross section is perpendicular to the x-axis. And it is a disc with radius r=x because it is the distance from the line OB(y=x)  to the axis of rotationOA (y=0).

From the figure, the solid lies between x=0 and  x=1

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