Chapter 15.3, Problem 14E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Evaluate the given integral by changing to polar coordinates.

**14.**
*D* is the region in the first quadrant that lies between the circles *x*^{2} + *y*^{2} = 4 and *x*^{2} + *y*^{2} = 2*x*

To determine

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

Explanation

**Given:**

The function,

The region *D* is lies between the circles

**Formula used:**

If
*R* given by

If

**Calculation:**

From the given region *D*, it is observed that the value of *r* varies from 0 to 2 and the value of
*D* lies between the two given curves.

Substitute

Integrate the function with respect to
*r* by using the equation (2).

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