Chapter 8.2, Problem 3E

BuyFind*arrow_forward*

8th Edition

James Stewart

ISBN: 9781305270336

Textbook Problem

- (a) Set up an integral for the area of the surface obtained by rotating the curve about (i) the
*x*-axis and (ii) the*y*-axis. - (b) Use the numerical integration capability of a calculator to evaluate the surface areas correct to four decimal places.

**3.**
*x* ≤ 1

(a)

(i)

To determine

**To set up:** An integral for the area of the surface obtained by rotating the curve about *x*-axis.

Explanation

**Given:**

The equation of the curve is

**Calculation:**

Given the equation of the curve.

Calculate the area of the surface obtained by rotating the curve about *x*-axis using the relation:

Here, *S* is the area of the surface obtained by rotating the curve about *x*-axis and

Consider the value of the function

Substitute *u* for

Differentiate Equation (4) with respect to *u*.

Differentiate Equation (3) with respect to *x*.

Calculate the value of

Substitute

(ii)

To determine

**To set up:** An integral for the area of the surface obtained by rotating the curve about *y*-axis.

(b)

(i)

To determine

**To evaluate:** The surface area of the curve about *x*-axis by using the numerical integration capability of the calculator.

(ii)

To determine

**To evaluate:** The surface area of the curve about *y*-axis by using numerical integration capability of the calculator.

Sect-8.1 P-1ESect-8.1 P-2ESect-8.1 P-3ESect-8.1 P-4ESect-8.1 P-5ESect-8.1 P-6ESect-8.1 P-7ESect-8.1 P-8ESect-8.1 P-9ESect-8.1 P-10E

Sect-8.1 P-11ESect-8.1 P-12ESect-8.1 P-13ESect-8.1 P-14ESect-8.1 P-15ESect-8.1 P-16ESect-8.1 P-17ESect-8.1 P-18ESect-8.1 P-19ESect-8.1 P-20ESect-8.1 P-21ESect-8.1 P-22ESect-8.1 P-23ESect-8.1 P-24ESect-8.1 P-25ESect-8.1 P-26ESect-8.1 P-27ESect-8.1 P-28ESect-8.1 P-29ESect-8.1 P-30ESect-8.1 P-33ESect-8.1 P-34ESect-8.1 P-35ESect-8.1 P-36ESect-8.1 P-37ESect-8.1 P-38ESect-8.1 P-39ESect-8.1 P-40ESect-8.1 P-41ESect-8.1 P-42ESect-8.1 P-43ESect-8.1 P-44ESect-8.1 P-45ESect-8.1 P-46ESect-8.2 P-1ESect-8.2 P-2ESect-8.2 P-3ESect-8.2 P-4ESect-8.2 P-5ESect-8.2 P-6ESect-8.2 P-7ESect-8.2 P-8ESect-8.2 P-9ESect-8.2 P-10ESect-8.2 P-11ESect-8.2 P-12ESect-8.2 P-13ESect-8.2 P-14ESect-8.2 P-15ESect-8.2 P-16ESect-8.2 P-17ESect-8.2 P-18ESect-8.2 P-19ESect-8.2 P-20ESect-8.2 P-21ESect-8.2 P-22ESect-8.2 P-23ESect-8.2 P-24ESect-8.2 P-27ESect-8.2 P-28ESect-8.2 P-29ESect-8.2 P-30ESect-8.2 P-31ESect-8.2 P-32ESect-8.2 P-33ESect-8.2 P-35ESect-8.2 P-36ESect-8.2 P-37ESect-8.2 P-38ESect-8.2 P-39ESect-8.3 P-1ESect-8.3 P-2ESect-8.3 P-3ESect-8.3 P-4ESect-8.3 P-5ESect-8.3 P-6ESect-8.3 P-7ESect-8.3 P-8ESect-8.3 P-9ESect-8.3 P-10ESect-8.3 P-11ESect-8.3 P-12ESect-8.3 P-13ESect-8.3 P-14ESect-8.3 P-15ESect-8.3 P-16ESect-8.3 P-17ESect-8.3 P-18ESect-8.3 P-19ESect-8.3 P-20ESect-8.3 P-21ESect-8.3 P-22ESect-8.3 P-23ESect-8.3 P-24ESect-8.3 P-25ESect-8.3 P-26ESect-8.3 P-27ESect-8.3 P-28ESect-8.3 P-29ESect-8.3 P-30ESect-8.3 P-31ESect-8.3 P-32ESect-8.3 P-33ESect-8.3 P-34ESect-8.3 P-35ESect-8.3 P-36ESect-8.3 P-37ESect-8.3 P-38ESect-8.3 P-39ESect-8.3 P-40ESect-8.3 P-41ESect-8.3 P-42ESect-8.3 P-43ESect-8.3 P-44ESect-8.3 P-45ESect-8.3 P-46ESect-8.3 P-47ESect-8.3 P-48ESect-8.3 P-49ESect-8.3 P-50ESect-8.3 P-51ESect-8.4 P-1ESect-8.4 P-2ESect-8.4 P-3ESect-8.4 P-4ESect-8.4 P-5ESect-8.4 P-6ESect-8.4 P-7ESect-8.4 P-8ESect-8.4 P-9ESect-8.4 P-10ESect-8.4 P-11ESect-8.4 P-12ESect-8.4 P-13ESect-8.4 P-14ESect-8.4 P-15ESect-8.4 P-16ESect-8.4 P-17ESect-8.4 P-18ESect-8.4 P-19ESect-8.4 P-20ESect-8.4 P-21ESect-8.4 P-22ESect-8.4 P-23ESect-8.5 P-1ESect-8.5 P-2ESect-8.5 P-3ESect-8.5 P-4ESect-8.5 P-5ESect-8.5 P-6ESect-8.5 P-7ESect-8.5 P-8ESect-8.5 P-9ESect-8.5 P-10ESect-8.5 P-11ESect-8.5 P-12ESect-8.5 P-13ESect-8.5 P-14ESect-8.5 P-15ESect-8.5 P-16ESect-8.5 P-17ESect-8.5 P-18ESect-8.5 P-19ESect-8.5 P-20ESect-8.5 P-21ECh-8 P-1RCCCh-8 P-2RCCCh-8 P-3RCCCh-8 P-4RCCCh-8 P-5RCCCh-8 P-6RCCCh-8 P-7RCCCh-8 P-8RCCCh-8 P-9RCCCh-8 P-10RCCCh-8 P-1RECh-8 P-2RECh-8 P-3RECh-8 P-4RECh-8 P-5RECh-8 P-6RECh-8 P-7RECh-8 P-8RECh-8 P-9RECh-8 P-10RECh-8 P-11RECh-8 P-12RECh-8 P-13RECh-8 P-14RECh-8 P-15RECh-8 P-16RECh-8 P-17RECh-8 P-18RECh-8 P-19RECh-8 P-20RECh-8 P-21RECh-8 P-22RECh-8 P-23RECh-8 P-1PCh-8 P-2PCh-8 P-3PCh-8 P-4PCh-8 P-5PCh-8 P-6PCh-8 P-7PCh-8 P-8PCh-8 P-9PCh-8 P-10PCh-8 P-11PCh-8 P-12PCh-8 P-13P

Calculus: Early Transcendental Functions

Calculus (MindTap Course List)

Applied Calculus

Precalculus: Mathematics for Calculus (Standalone Book)

Calculus: Early Transcendentals

Multivariable Calculus

Single Variable Calculus

Finite Mathematics and Applied Calculus (MindTap Course List)

Single Variable Calculus: Early Transcendentals, Volume I

Calculus (MindTap Course List)

Calculus: An Applied Approach (MindTap Course List)

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

Probability and Statistics for Engineering and the Sciences

Contemporary Mathematics for Business & Consumers

Mathematical Excursions (MindTap Course List)

Statistics for The Behavioral Sciences (MindTap Course List)

Intermediate Algebra

Essentials Of Statistics

Understanding Basic Statistics

Finite Mathematics

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

Mathematical Applications for the Management, Life, and Social Sciences

Trigonometry (MindTap Course List)

Elementary Technical Mathematics

Elements Of Modern Algebra

Elementary Geometry For College Students, 7e

Calculus: Early Transcendental Functions (MindTap Course List)

Calculus of a Single Variable

Finite Mathematics for the Managerial, Life, and Social Sciences

Elementary Geometry for College Students

Multivariable Calculus

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

Study Guide for Stewart's Multivariable Calculus, 8th

Mathematics For Machine Technology

College Algebra (MindTap Course List)

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Introduction To Statistics And Data Analysis

Research Methods for the Behavioral Sciences (MindTap Course List)

Research Methods for the Behavioral Sciences (MindTap Course List)

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