Chapter 15.6, Problem 2E

BuyFind*arrow_forward*

8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Evaluate the integral

**3-8** Evaluate the iterated integral.

To determine

**To evaluate:** The integral of

Explanation

**Given:**

The function is

The region is

**Calculation:**

**Case 1:** Order of integration is *x*, *y* and *z*.

The given integral with the above order is,

Integrate the given integral with respect to *x* and apply the limit of it.

Integrate the given integral with respect to *y* and apply the limit of it.

Integrate the given integral with respect to *z* and apply the limit of it.

Simplify further to obtain the value.

Thus, the value of the integral with the order *x,y* and *z* is 21.

**Case 2:**

Order of integration proceed with the order *y*, then *z* and *x*.

The given integral with the above order is,

Integrate the given integral with respect to *y* and apply the limit of it.

Integrate the given integral with respect to *z* and apply the limit of it

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

Finite Mathematics and Applied Calculus (MindTap Course List)

Multivariable Calculus

Calculus: An Applied Approach (MindTap Course List)

Precalculus: Mathematics for Calculus (Standalone Book)

Calculus: Early Transcendental Functions

Applied Calculus

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)

Single Variable Calculus

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

Finite Mathematics

Understanding Basic Statistics

Probability and Statistics for Engineering and the Sciences

Elementary Geometry For College Students, 7e

Contemporary Mathematics for Business & Consumers

Mathematical Applications for the Management, Life, and Social Sciences

Mathematical Excursions (MindTap Course List)

Elementary Technical Mathematics

Intermediate Algebra

Single Variable Calculus: Early Transcendentals

Calculus of a Single Variable

Calculus: Early Transcendental Functions (MindTap Course List)

Trigonometry (MindTap Course List)

Elements Of Modern Algebra

Study Guide for Stewart's Multivariable Calculus, 8th

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

Finite Mathematics for the Managerial, Life, and Social Sciences

Elementary Geometry for College Students