Chapter 5.R, Problem 9E

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.

To determine

**To find:**

The volume of the solid obtained by rotating the region bounded by the given curves about the specified line and sketch the region, the solid, and a typical disk or washer.

Explanation

**1) Concept:**

i. If the cross section is a washer with the inner radius

ii. The volume of solid revolution about

**2) Given:**

The region is bounded by

**3) Calculation:**

As the region is bounded by

From the figure, as the region rotates about the line

A cross section of the solid is the washer with outer radius is

So its area is given by

The region of integration is bounded by

Therefore,

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