Chapter 15.3, Problem 32E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Evaluate the iterated integral by converting to polar coordinates.

**32.**

To determine

**To evaluate:** The iterated integral using polar coordinates.

Explanation

**Given:**

The function is,

The variable *x* varies from 0 to 2 and *y* varies from 0 to

**Formula used:**

If
*R* given by

**Calculation:**

In order to convert the given function into polar coordinates, substitute
*z* becomes,

Moreover, from the given condition of *x* and *y*, the value of *r* varies from 0 to

Therefore, by the equation (1), the value of the iterated integral becomes,

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

On further simplification, the integral value becomes,

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