Chapter 15.3, Problem 3E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

A region *R* is shown. Decide whether to use polar coordinates or rectangular coordinates and write
*f* is an arbitrary continuous function on *R*.

**3.**

To determine

**To write:** An iterated integral by deciding whether to use polar coordinates or rectangular coordinates.

Explanation

**Formula used:**

If
*R* given by

**Calculation:**

Since the given region is the semicircle, it is easier to use polar coordinates.

From the figure given in the problem, it is observed that radius *r* ranges from 0 to 1 and

Therefore, the polar coordinates is,

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