Chapter 15.3, Problem 34E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Express the double integral in terms of a single integral with respect to *r.* Then use your calculator to evaluate the integral correct to four decimal places.

**34.**
*D* is the portion of the disk *x*^{2} + *y*^{2} ≤ 1 that lies in the first quadrant

To determine

**To evaluate:** The value of the double integral using calculator.

Explanation

**Given:**

The function is,

The region *D* is the portion of the disk

**Formula used:**

If *R* given by

If

**Calculation:**

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

And, from the given region *D*, *r* varies from 0 to 1 and

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

Integrate the function with respect to *r* and

Let

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