Chapter 15.3, Problem 39E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Use polar coordinates to combine the sum

To determine

**To evaluate:** The given double integral by changing into the polar coordinates.

Explanation

**Given:**

The function,

**Formula used:**

If *R* given by

If

**Calculation:**

From the limit points of the given three integrals, draw the figures as given below.

From the three figures (Figure1, Figure2, and Figure3), it is observed that the union is the annular region of the two disks whose radius is 1 and 2, respectively.

Therefore, *r* varies from 1 to 2 and

Substitute

Therefore, by the equation (1) the given integral becomes,

Integrate the function with respect to *r* and

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