   Chapter 5.2, Problem 26E

Chapter
Section
Textbook Problem

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