Chapter 5.3, Problem 14E

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the *x*-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:**

The region bounded by

**3) Calculation:**

As the region is bounded by

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

To find the height of the strip, subtract the above functions.

Therefore, the circumference is

To find the point of intersections,

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