Chapter 15.3, Problem 17E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Use a double integral to find the area of the region.

**17.** The region inside the circle (*x* − 1)^{2} + *y*^{2} = 1 and outside the circle *x*^{2} + *y*^{2} = 1

To determine

**To find:** The area of the region using double integral.

Explanation

**Given:**

The region *D* lies inside the circle

**Formula used:**

If
*R* given by

**Calculation:**

From the given region *D*, obtain the value of *r*.

It is observed that the value of *r* varies from 1 to

Therefore,

Substitute

Integrate with respect to *r* and apply the limit as shown below

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