Chapter 5.3, Problem 20E

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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

whereÂ

iii. The theorem of symmetric function:

Suppose

(a) If

(b) If

**2) Given:**

**3) Calculation:**

As the region is bounded by

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

It has the radius

Using the shell method, to find the typical approximating shell with the radius

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