Chapter 5.3, Problem 17E

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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

**2) Given:**

**3) Calculation:**

As the region is bounded by

The graph shows the region and the vertical cross section of cylindrical shell formed by the rotation about the line

It has the radius

Therefore, the circumference is

To find the point of intersection, equate both curves

This is a quadratic equation.

Solve by using the quadratic formula

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