Chapter 15.3, Problem 10E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Evaluate the given integral by changing to polar coordinates.

**10.**
*R* is the region that lies between the circles *x*^{2} + *y*^{2} = *a*^{2} and *x*^{2} + *y*^{2} = *b*^{2} with 0 < *a* < *b*

To determine

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

Explanation

**Given:**

The function,

The region *R* lies between the circles centered at origin and the radii *a* and *b*, respectively with 0 *< a < b.*

**Formula used:**

If
*R* given by

If

**Calculation:**

From the given region *R*, it is observed that the value of *r* varies from *a* to *b* and the value of

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

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

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