Chapter 5.3, Problem 15E

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the specified axis.

To determine

**To find:**

The volume generated by rotating the region bounded by the given curves about

Explanation

**1) Concept:**

i. If

ii. By the shell method, the volume of the solid by rotating the region under the curve

where,Â

**2) Given:**

**3) Calculation:**

As the region is bounded by

The graph shows the region and the cylindrical shell formed by rotation about the line

It has the radius

Using the shell method,

Find the typical approximating shell with radius

Therefore, circumference is

Find the points of intersection (the limit of integrals). At intersection

So

So,

So, the volume of the given solid is

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