Chapter 15.8, Problem 42E

BuyFind*arrow_forward*

8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Evaluate the integral by changing to spherical coordinates.

**42.**
* (x ^{2}z + y^{2}z* +

To determine

**To evaluate:** The integral by changing to spherical coordinates.

Explanation

**Given:**

The function is

The rectangular coordinates of the given triple integral are

**Formula used:**

If
*E* given by

If
*z* then,

The spherical coordinates

**Calculation:**

Substitute

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

Sect-15.1 P-11ESect-15.1 P-12ESect-15.1 P-13ESect-15.1 P-14ESect-15.1 P-15ESect-15.1 P-16ESect-15.1 P-17ESect-15.1 P-18ESect-15.1 P-19ESect-15.1 P-20ESect-15.1 P-21ESect-15.1 P-22ESect-15.1 P-23ESect-15.1 P-24ESect-15.1 P-25ESect-15.1 P-26ESect-15.1 P-27ESect-15.1 P-28ESect-15.1 P-29ESect-15.1 P-30ESect-15.1 P-31ESect-15.1 P-32ESect-15.1 P-33ESect-15.1 P-34ESect-15.1 P-35ESect-15.1 P-36ESect-15.1 P-37ESect-15.1 P-38ESect-15.1 P-39ESect-15.1 P-40ESect-15.1 P-41ESect-15.1 P-42ESect-15.1 P-43ESect-15.1 P-44ESect-15.1 P-47ESect-15.1 P-48ESect-15.1 P-49ESect-15.1 P-50ESect-15.1 P-52ESect-15.2 P-1ESect-15.2 P-2ESect-15.2 P-3ESect-15.2 P-4ESect-15.2 P-5ESect-15.2 P-6ESect-15.2 P-7ESect-15.2 P-8ESect-15.2 P-9ESect-15.2 P-10ESect-15.2 P-11ESect-15.2 P-12ESect-15.2 P-13ESect-15.2 P-14ESect-15.2 P-15ESect-15.2 P-16ESect-15.2 P-17ESect-15.2 P-18ESect-15.2 P-19ESect-15.2 P-20ESect-15.2 P-21ESect-15.2 P-22ESect-15.2 P-23ESect-15.2 P-24ESect-15.2 P-25ESect-15.2 P-26ESect-15.2 P-27ESect-15.2 P-28ESect-15.2 P-29ESect-15.2 P-30ESect-15.2 P-31ESect-15.2 P-32ESect-15.2 P-33ESect-15.2 P-34ESect-15.2 P-35ESect-15.2 P-36ESect-15.2 P-37ESect-15.2 P-38ESect-15.2 P-39ESect-15.2 P-40ESect-15.2 P-45ESect-15.2 P-46ESect-15.2 P-47ESect-15.2 P-48ESect-15.2 P-49ESect-15.2 P-50ESect-15.2 P-51ESect-15.2 P-52ESect-15.2 P-53ESect-15.2 P-54ESect-15.2 P-55ESect-15.2 P-56ESect-15.2 P-57ESect-15.2 P-58ESect-15.2 P-59ESect-15.2 P-60ESect-15.2 P-61ESect-15.2 P-62ESect-15.2 P-63ESect-15.2 P-64ESect-15.2 P-65ESect-15.2 P-66ESect-15.2 P-67ESect-15.2 P-68ESect-15.2 P-69ESect-15.3 P-1ESect-15.3 P-2ESect-15.3 P-3ESect-15.3 P-4ESect-15.3 P-5ESect-15.3 P-6ESect-15.3 P-7ESect-15.3 P-8ESect-15.3 P-9ESect-15.3 P-10ESect-15.3 P-11ESect-15.3 P-12ESect-15.3 P-13ESect-15.3 P-14ESect-15.3 P-15ESect-15.3 P-16ESect-15.3 P-17ESect-15.3 P-18ESect-15.3 P-19ESect-15.3 P-20ESect-15.3 P-21ESect-15.3 P-22ESect-15.3 P-23ESect-15.3 P-24ESect-15.3 P-25ESect-15.3 P-26ESect-15.3 P-27ESect-15.3 P-28ESect-15.3 P-29ESect-15.3 P-30ESect-15.3 P-31ESect-15.3 P-32ESect-15.3 P-33ESect-15.3 P-34ESect-15.3 P-35ESect-15.3 P-36ESect-15.3 P-37ESect-15.3 P-38ESect-15.3 P-39ESect-15.3 P-40ESect-15.3 P-41ESect-15.4 P-1ESect-15.4 P-2ESect-15.4 P-3ESect-15.4 P-4ESect-15.4 P-5ESect-15.4 P-6ESect-15.4 P-7ESect-15.4 P-8ESect-15.4 P-9ESect-15.4 P-10ESect-15.4 P-11ESect-15.4 P-12ESect-15.4 P-13ESect-15.4 P-14ESect-15.4 P-15ESect-15.4 P-16ESect-15.4 P-17ESect-15.4 P-18ESect-15.4 P-19ESect-15.4 P-20ESect-15.4 P-21ESect-15.4 P-22ESect-15.4 P-23ESect-15.4 P-24ESect-15.4 P-27ESect-15.4 P-28ESect-15.4 P-29ESect-15.4 P-30ESect-15.4 P-32ESect-15.4 P-33ESect-15.5 P-1ESect-15.5 P-2ESect-15.5 P-3ESect-15.5 P-4ESect-15.5 P-5ESect-15.5 P-6ESect-15.5 P-7ESect-15.5 P-8ESect-15.5 P-9ESect-15.5 P-10ESect-15.5 P-11ESect-15.5 P-12ESect-15.5 P-13ESect-15.5 P-14ESect-15.5 P-21ESect-15.5 P-22ESect-15.5 P-23ESect-15.5 P-24ESect-15.6 P-1ESect-15.6 P-2ESect-15.6 P-3ESect-15.6 P-4ESect-15.6 P-5ESect-15.6 P-6ESect-15.6 P-7ESect-15.6 P-8ESect-15.6 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 P-26ESect-15.7 P-27ESect-15.7 P-28ESect-15.7 P-29ESect-15.7 P-30ESect-15.7 P-31ESect-15.8 P-1ESect-15.8 P-2ESect-15.8 P-3ESect-15.8 P-4ESect-15.8 P-5ESect-15.8 P-6ESect-15.8 P-7ESect-15.8 P-8ESect-15.8 P-9ESect-15.8 P-10ESect-15.8 P-11ESect-15.8 P-12ESect-15.8 P-13ESect-15.8 P-14ESect-15.8 P-15ESect-15.8 P-16ESect-15.8 P-17ESect-15.8 P-18ESect-15.8 P-19ESect-15.8 P-20ESect-15.8 P-21ESect-15.8 P-22ESect-15.8 P-23ESect-15.8 P-24ESect-15.8 P-25ESect-15.8 P-26ESect-15.8 P-27ESect-15.8 P-28ESect-15.8 P-29ESect-15.8 P-30ESect-15.8 P-31ESect-15.8 P-32ESect-15.8 P-33ESect-15.8 P-34ESect-15.8 P-35ESect-15.8 P-36ESect-15.8 P-37ESect-15.8 P-38ESect-15.8 P-41ESect-15.8 P-42ESect-15.8 P-43ESect-15.8 P-44ESect-15.8 P-45ESect-15.8 P-46ESect-15.8 P-48ESect-15.8 P-49ESect-15.9 P-1ESect-15.9 P-2ESect-15.9 P-3ESect-15.9 P-4ESect-15.9 P-5ESect-15.9 P-6ESect-15.9 P-7ESect-15.9 P-8ESect-15.9 P-9ESect-15.9 P-10ESect-15.9 P-11ESect-15.9 P-12ESect-15.9 P-13ESect-15.9 P-14ESect-15.9 P-15ESect-15.9 P-16ESect-15.9 P-17ESect-15.9 P-18ESect-15.9 P-19ESect-15.9 P-20ESect-15.9 P-21ESect-15.9 P-22ESect-15.9 P-23ESect-15.9 P-24ESect-15.9 P-25ESect-15.9 P-26ESect-15.9 P-27ESect-15.9 P-28ECh-15 P-1RCCCh-15 P-2RCCCh-15 P-3RCCCh-15 P-4RCCCh-15 P-5RCCCh-15 P-6RCCCh-15 P-7RCCCh-15 P-8RCCCh-15 P-9RCCCh-15 P-10RCCCh-15 P-1RQCh-15 P-2RQCh-15 P-3RQCh-15 P-4RQCh-15 P-5RQCh-15 P-6RQCh-15 P-7RQCh-15 P-8RQCh-15 P-9RQCh-15 P-1RECh-15 P-2RECh-15 P-3RECh-15 P-4RECh-15 P-5RECh-15 P-6RECh-15 P-7RECh-15 P-8RECh-15 P-9RECh-15 P-10RECh-15 P-11RECh-15 P-12RECh-15 P-13RECh-15 P-14RECh-15 P-15RECh-15 P-16RECh-15 P-17RECh-15 P-18RECh-15 P-19RECh-15 P-20RECh-15 P-21RECh-15 P-22RECh-15 P-23RECh-15 P-24RECh-15 P-25RECh-15 P-26RECh-15 P-27RECh-15 P-28RECh-15 P-29RECh-15 P-30RECh-15 P-31RECh-15 P-32RECh-15 P-33RECh-15 P-34RECh-15 P-35RECh-15 P-36RECh-15 P-37RECh-15 P-38RECh-15 P-39RECh-15 P-40RECh-15 P-41RECh-15 P-42RECh-15 P-43RECh-15 P-44RECh-15 P-45RECh-15 P-47RECh-15 P-48RECh-15 P-49RECh-15 P-51RECh-15 P-52RECh-15 P-53RECh-15 P-54RECh-15 P-55RECh-15 P-56RECh-15 P-57RECh-15 P-58RECh-15 P-59RECh-15 P-60RECh-15 P-1PCh-15 P-2PCh-15 P-3PCh-15 P-4PCh-15 P-5PCh-15 P-6PCh-15 P-7PCh-15 P-8PCh-15 P-9PCh-15 P-10PCh-15 P-11PCh-15 P-12PCh-15 P-13P

Precalculus: Mathematics for Calculus (Standalone Book)

Calculus: Early Transcendental Functions

Multivariable Calculus

Calculus: An Applied Approach (MindTap Course List)

Finite Mathematics and Applied Calculus (MindTap Course List)

Single Variable Calculus: Early Transcendentals, Volume I

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Essentials Of Statistics

Calculus (MindTap Course List)

Statistics for The Behavioral Sciences (MindTap Course List)

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Single Variable Calculus

Understanding Basic Statistics

Finite Mathematics

Probability and Statistics for Engineering and the Sciences

Elementary Technical Mathematics

Intermediate Algebra

Contemporary Mathematics for Business & Consumers

Mathematical Excursions (MindTap Course List)

Mathematical Applications for the Management, Life, and Social Sciences

Elementary Geometry For College Students, 7e

Calculus: Early Transcendental Functions (MindTap Course List)

Calculus of a Single Variable

Single Variable Calculus: Early Transcendentals

Trigonometry (MindTap Course List)

Elements Of Modern Algebra

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Study Guide for Stewart's Multivariable Calculus, 8th

Elementary Geometry for College Students

Finite Mathematics for the Managerial, Life, and Social Sciences