Chapter 16, Problem 8RE

BuyFind*arrow_forward*

8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Evaluate the line integral.

**8.** ∫* _{C}* F ·

To determine

**To Evaluate:** The line integral

Explanation

**Given data:**

**Formula used:**

Write the expression for

Write the required differential formulae to evaluate the given integral.

Write the required integration formulae to evaluate the given integral.

Write the standard formula.

Consider the expression for

Compare equations (1) and (2).

Consider the expression for

Substitute

Differentiate equation (2) with respect to

Find the value of

Change the limits with respect to

Sect-16.1 P-1ESect-16.1 P-2ESect-16.1 P-3ESect-16.1 P-4ESect-16.1 P-5ESect-16.1 P-6ESect-16.1 P-7ESect-16.1 P-8ESect-16.1 P-9ESect-16.1 P-10E

Sect-16.1 P-11ESect-16.1 P-12ESect-16.1 P-13ESect-16.1 P-14ESect-16.1 P-15ESect-16.1 P-16ESect-16.1 P-17ESect-16.1 P-18ESect-16.1 P-21ESect-16.1 P-22ESect-16.1 P-23ESect-16.1 P-24ESect-16.1 P-25ESect-16.1 P-26ESect-16.1 P-29ESect-16.1 P-30ESect-16.1 P-31ESect-16.1 P-32ESect-16.1 P-33ESect-16.1 P-34ESect-16.1 P-35ESect-16.1 P-36ESect-16.2 P-1ESect-16.2 P-2ESect-16.2 P-3ESect-16.2 P-4ESect-16.2 P-5ESect-16.2 P-6ESect-16.2 P-7ESect-16.2 P-8ESect-16.2 P-9ESect-16.2 P-10ESect-16.2 P-11ESect-16.2 P-12ESect-16.2 P-13ESect-16.2 P-14ESect-16.2 P-15ESect-16.2 P-16ESect-16.2 P-17ESect-16.2 P-18ESect-16.2 P-19ESect-16.2 P-20ESect-16.2 P-21ESect-16.2 P-22ESect-16.2 P-23ESect-16.2 P-24ESect-16.2 P-25ESect-16.2 P-26ESect-16.2 P-31ESect-16.2 P-32ESect-16.2 P-33ESect-16.2 P-34ESect-16.2 P-35ESect-16.2 P-36ESect-16.2 P-37ESect-16.2 P-38ESect-16.2 P-39ESect-16.2 P-40ESect-16.2 P-41ESect-16.2 P-42ESect-16.2 P-43ESect-16.2 P-44ESect-16.2 P-45ESect-16.2 P-46ESect-16.2 P-47ESect-16.2 P-48ESect-16.2 P-49ESect-16.2 P-50ESect-16.2 P-51ESect-16.2 P-52ESect-16.3 P-1ESect-16.3 P-2ESect-16.3 P-3ESect-16.3 P-4ESect-16.3 P-5ESect-16.3 P-6ESect-16.3 P-7ESect-16.3 P-8ESect-16.3 P-9ESect-16.3 P-10ESect-16.3 P-11ESect-16.3 P-12ESect-16.3 P-13ESect-16.3 P-14ESect-16.3 P-15ESect-16.3 P-16ESect-16.3 P-17ESect-16.3 P-18ESect-16.3 P-19ESect-16.3 P-20ESect-16.3 P-21ESect-16.3 P-22ESect-16.3 P-23ESect-16.3 P-24ESect-16.3 P-25ESect-16.3 P-26ESect-16.3 P-28ESect-16.3 P-29ESect-16.3 P-30ESect-16.3 P-31ESect-16.3 P-32ESect-16.3 P-33ESect-16.3 P-34ESect-16.3 P-35ESect-16.4 P-1ESect-16.4 P-2ESect-16.4 P-3ESect-16.4 P-4ESect-16.4 P-5ESect-16.4 P-6ESect-16.4 P-7ESect-16.4 P-8ESect-16.4 P-9ESect-16.4 P-10ESect-16.4 P-11ESect-16.4 P-12ESect-16.4 P-13ESect-16.4 P-14ESect-16.4 P-17ESect-16.4 P-18ESect-16.4 P-19ESect-16.4 P-20ESect-16.4 P-21ESect-16.4 P-22ESect-16.4 P-23ESect-16.4 P-24ESect-16.4 P-25ESect-16.4 P-26ESect-16.4 P-27ESect-16.4 P-28ESect-16.4 P-29ESect-16.4 P-30ESect-16.4 P-31ESect-16.5 P-1ESect-16.5 P-2ESect-16.5 P-3ESect-16.5 P-4ESect-16.5 P-5ESect-16.5 P-6ESect-16.5 P-7ESect-16.5 P-8ESect-16.5 P-9ESect-16.5 P-10ESect-16.5 P-11ESect-16.5 P-12ESect-16.5 P-13ESect-16.5 P-14ESect-16.5 P-15ESect-16.5 P-16ESect-16.5 P-17ESect-16.5 P-18ESect-16.5 P-19ESect-16.5 P-20ESect-16.5 P-21ESect-16.5 P-22ESect-16.5 P-23ESect-16.5 P-24ESect-16.5 P-25ESect-16.5 P-26ESect-16.5 P-27ESect-16.5 P-28ESect-16.5 P-29ESect-16.5 P-30ESect-16.5 P-31ESect-16.5 P-32ESect-16.5 P-33ESect-16.5 P-34ESect-16.5 P-35ESect-16.5 P-36ESect-16.5 P-37ESect-16.5 P-38ESect-16.5 P-39ESect-16.6 P-1ESect-16.6 P-2ESect-16.6 P-3ESect-16.6 P-4ESect-16.6 P-5ESect-16.6 P-6ESect-16.6 P-13ESect-16.6 P-14ESect-16.6 P-15ESect-16.6 P-16ESect-16.6 P-17ESect-16.6 P-18ESect-16.6 P-19ESect-16.6 P-20ESect-16.6 P-21ESect-16.6 P-22ESect-16.6 P-23ESect-16.6 P-24ESect-16.6 P-25ESect-16.6 P-26ESect-16.6 P-29ESect-16.6 P-30ESect-16.6 P-33ESect-16.6 P-34ESect-16.6 P-35ESect-16.6 P-36ESect-16.6 P-37ESect-16.6 P-38ESect-16.6 P-39ESect-16.6 P-40ESect-16.6 P-41ESect-16.6 P-42ESect-16.6 P-43ESect-16.6 P-44ESect-16.6 P-45ESect-16.6 P-46ESect-16.6 P-47ESect-16.6 P-48ESect-16.6 P-49ESect-16.6 P-50ESect-16.6 P-51ESect-16.6 P-52ESect-16.6 P-53ESect-16.6 P-54ESect-16.6 P-56ESect-16.6 P-59ESect-16.6 P-60ESect-16.6 P-61ESect-16.6 P-62ESect-16.6 P-63ESect-16.7 P-1ESect-16.7 P-2ESect-16.7 P-3ESect-16.7 P-4ESect-16.7 P-5ESect-16.7 P-6ESect-16.7 P-7ESect-16.7 P-8ESect-16.7 P-9ESect-16.7 P-10ESect-16.7 P-11ESect-16.7 P-12ESect-16.7 P-13ESect-16.7 P-14ESect-16.7 P-15ESect-16.7 P-16ESect-16.7 P-17ESect-16.7 P-18ESect-16.7 P-19ESect-16.7 P-20ESect-16.7 P-21ESect-16.7 P-22ESect-16.7 P-23ESect-16.7 P-24ESect-16.7 P-25ESect-16.7 P-26ESect-16.7 P-28ESect-16.7 P-37ESect-16.7 P-38ESect-16.7 P-39ESect-16.7 P-40ESect-16.7 P-41ESect-16.7 P-42ESect-16.7 P-43ESect-16.7 P-44ESect-16.7 P-45ESect-16.7 P-46ESect-16.7 P-47ESect-16.7 P-48ESect-16.7 P-49ESect-16.8 P-1ESect-16.8 P-2ESect-16.8 P-3ESect-16.8 P-4ESect-16.8 P-5ESect-16.8 P-6ESect-16.8 P-7ESect-16.8 P-8ESect-16.8 P-9ESect-16.8 P-10ESect-16.8 P-11ESect-16.8 P-12ESect-16.8 P-13ESect-16.8 P-14ESect-16.8 P-15ESect-16.8 P-17ESect-16.8 P-18ESect-16.8 P-19ESect-16.8 P-20ESect-16.9 P-1ESect-16.9 P-2ESect-16.9 P-3ESect-16.9 P-4ESect-16.9 P-5ESect-16.9 P-6ESect-16.9 P-7ESect-16.9 P-8ESect-16.9 P-9ESect-16.9 P-10ESect-16.9 P-11ESect-16.9 P-12ESect-16.9 P-13ESect-16.9 P-14ESect-16.9 P-17ESect-16.9 P-18ESect-16.9 P-19ESect-16.9 P-20ESect-16.9 P-23ESect-16.9 P-24ESect-16.9 P-25ESect-16.9 P-26ESect-16.9 P-27ESect-16.9 P-28ESect-16.9 P-29ESect-16.9 P-30ESect-16.9 P-31ESect-16.9 P-32ECh-16 P-1RCCCh-16 P-2RCCCh-16 P-3RCCCh-16 P-4RCCCh-16 P-5RCCCh-16 P-6RCCCh-16 P-7RCCCh-16 P-8RCCCh-16 P-9RCCCh-16 P-10RCCCh-16 P-11RCCCh-16 P-12RCCCh-16 P-13RCCCh-16 P-14RCCCh-16 P-15RCCCh-16 P-16RCCCh-16 P-1RQCh-16 P-2RQCh-16 P-3RQCh-16 P-4RQCh-16 P-5RQCh-16 P-6RQCh-16 P-7RQCh-16 P-8RQCh-16 P-9RQCh-16 P-10RQCh-16 P-11RQCh-16 P-12RQCh-16 P-13RQCh-16 P-1RECh-16 P-2RECh-16 P-3RECh-16 P-4RECh-16 P-5RECh-16 P-6RECh-16 P-7RECh-16 P-8RECh-16 P-9RECh-16 P-10RECh-16 P-11RECh-16 P-12RECh-16 P-13RECh-16 P-14RECh-16 P-15RECh-16 P-16RECh-16 P-17RECh-16 P-18RECh-16 P-19RECh-16 P-20RECh-16 P-21RECh-16 P-22RECh-16 P-23RECh-16 P-24RECh-16 P-25RECh-16 P-27RECh-16 P-28RECh-16 P-29RECh-16 P-30RECh-16 P-31RECh-16 P-32RECh-16 P-33RECh-16 P-34RECh-16 P-35RECh-16 P-36RECh-16 P-37RECh-16 P-38RECh-16 P-39RECh-16 P-40RECh-16 P-41RECh-16 P-1PCh-16 P-2PCh-16 P-3PCh-16 P-5PCh-16 P-6P

Calculus: Early Transcendental Functions

Single Variable Calculus: Early Transcendentals, Volume I

Precalculus: Mathematics for Calculus (Standalone Book)

Calculus: An Applied Approach (MindTap Course List)

Multivariable Calculus

Applied Calculus

Finite Mathematics and Applied Calculus (MindTap Course List)

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

Probability and Statistics for Engineering and the Sciences

Understanding Basic Statistics

Finite Mathematics

Mathematical Excursions (MindTap Course List)

Elementary Geometry For College Students, 7e

Mathematical Applications for the Management, Life, and Social Sciences

Intermediate Algebra

Contemporary Mathematics for Business & Consumers

Elementary Technical Mathematics

Calculus of a Single Variable

Single Variable Calculus: Early Transcendentals

Calculus: Early Transcendental Functions (MindTap Course List)

Elements Of Modern Algebra

Trigonometry (MindTap Course List)

Study Guide for Stewart's Multivariable Calculus, 8th

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

Elementary Geometry for College Students

Finite Mathematics for the Managerial, Life, and Social Sciences

Multivariable Calculus

Calculus (MindTap Course List)

College Algebra (MindTap Course List)

Research Methods for the Behavioral Sciences (MindTap Course List)

Introduction To Statistics And Data Analysis

Statistics for Business & Economics, Revised (MindTap Course List)

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Mathematics For Machine Technology

Research Methods for the Behavioral Sciences (MindTap Course List)