   Chapter 5.3, Problem 39E

Chapter
Section
Textbook Problem

# The region bounded by the given curves is rotated about the specified axis. Find the volume of the resulting solid by any method. y 2 − x 2 = 1 ,   y = 2 ;    about the  x -axis

To determine

To find:

The volume of the solid obtained by rotating the region bounded by the given curves about the specified line.

Explanation

1) Concept:

The volume of the washer obtained by the revolution about the x-axis is

2) Given:

The region bounded by y2-x2=1, y=2,  rotated about the x- axis.

3) Calculation:

The graph of the region bounded by the given curves is

Find the volume of the solid by using the washer method.

Here, the region is bounded by  y2-x2=1y=±x2+1 and y=2

The outer radius is y=2 and the inner radius is x2+1. At intersection of both curves x2+1=2 That is x2+1=4

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