Chapter 15.2, Problem 65E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Use geometry or symmetry, or both, to evaluate the double integral.

**65.**

To determine

**To calculate:** The value of given double integral over
*.*

Explanation

**Given**

The function is,

The domain is,

**Definition used:**

Odd function: If

**Formula used:**

If

Thus,

**Calculation:**

The value of the given double integral is,

From (1), first term will become 0

Sect-15.1 P-1ESect-15.1 P-2ESect-15.1 P-3ESect-15.1 P-4ESect-15.1 P-5ESect-15.1 P-6ESect-15.1 P-7ESect-15.1 P-8ESect-15.1 P-9ESect-15.1 P-10E

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P-9ESect-15.6 P-10ESect-15.6 P-11ESect-15.6 P-12ESect-15.6 P-13ESect-15.6 P-14ESect-15.6 P-15ESect-15.6 P-16ESect-15.6 P-17ESect-15.6 P-18ESect-15.6 P-19ESect-15.6 P-20ESect-15.6 P-21ESect-15.6 P-22ESect-15.6 P-25ESect-15.6 P-26ESect-15.6 P-27ESect-15.6 P-28ESect-15.6 P-29ESect-15.6 P-30ESect-15.6 P-31ESect-15.6 P-32ESect-15.6 P-33ESect-15.6 P-34ESect-15.6 P-35ESect-15.6 P-36ESect-15.6 P-37ESect-15.6 P-38ESect-15.6 P-39ESect-15.6 P-40ESect-15.6 P-41ESect-15.6 P-42ESect-15.6 P-43ESect-15.6 P-44ESect-15.6 P-45ESect-15.6 P-46ESect-15.6 P-47ESect-15.6 P-48ESect-15.6 P-51ESect-15.6 P-52ESect-15.6 P-53ESect-15.6 P-54ESect-15.7 P-1ESect-15.7 P-2ESect-15.7 P-3ESect-15.7 P-4ESect-15.7 P-5ESect-15.7 P-6ESect-15.7 P-7ESect-15.7 P-8ESect-15.7 P-9ESect-15.7 P-10ESect-15.7 P-11ESect-15.7 P-12ESect-15.7 P-13ESect-15.7 P-14ESect-15.7 P-15ESect-15.7 P-16ESect-15.7 P-17ESect-15.7 P-18ESect-15.7 P-19ESect-15.7 P-20ESect-15.7 P-21ESect-15.7 P-22ESect-15.7 P-23ESect-15.7 P-24ESect-15.7 P-25ESect-15.7 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