Chapter 15, Problem 60RE

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

(a) Evaluate
*n* is an integer and *D* is the region bounded by the circles with center the origin and radii *r* and *R*, 0 < *r* < *R*.

(a)

To determine

**To evaluate:** The given integral.

Explanation

**Given:**

The function,

The region *D* lies between the circles centered at origin and the radii *r* and *R*, respectively.

**Formula used:**

If *R* given by

If

**Calculation:**

The radius of the smaller circle is denote the letter *r.* so, use the variable *t* for the polar coordinates instead of *r*. From the given region *D*, it is observed that the value of *t* varies from *r* to *R* and the value of

(b)

To determine

**To find:** For what values of the integer *n,* the integral in part (a) have a limit as

(c)

To determine

**To evaluate:** The given integral.

(d)

To determine

**To find:** For what values of the integer *n,* the integral in part (c) have a limit as

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