Chapter 5.3, Problem 24E

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

(a) Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curve about the specified axis.

(b) Use your calculator to evaluate the integral correct to five decimal places.

To determine

**a) **

**To find:**

The integral for the volume of the solid obtained by rotating the region bounded by the given curve about the specified axis.

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

Draw the region using the given curves.

The graph shows the region. A typical cylindrical shell is formed by the rotation about the line

It has the radius

Therefore, the circumference is

Now, to find the intersection points,

To determine

**b) **

**To evaluate:**

The integral ofthe volume of the solid.

Sect-5.1 P-1ESect-5.1 P-2ESect-5.1 P-3ESect-5.1 P-4ESect-5.1 P-5ESect-5.1 P-6ESect-5.1 P-7ESect-5.1 P-8ESect-5.1 P-9ESect-5.1 P-10E

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