Chapter 6.3, Problem 38E

BuyFind*arrow_forward*

10th Edition

Ron Larson

ISBN: 9781305860919

Textbook Problem

1 views

**Error Analysis** In Exercises 37-40, use the error formulas to find *n* such that the error in the approximation of the definite integral is less than 0.0001 using (a) the Trapezoidal Rule and (b) Simpson’s Rule. See *Example 3.*

**(a)**

To determine

**To calculate:** The value of

Explanation

**Given Information:**

The definite integral is

**Formula used:**

The simple power rule of differentiation,

The chain rule of differentiation for differential function

The quotient rule of differentiation,

The approximate value of integral

The approximate error in Trapezoidal Rule for integral

The steps to choose the value of *n* subdivision to calculate error:

Step:1. Find second derivative of function

Step:2. Find the maximum of

Step:3. The inequality for the error as,

Step:4

**(b)**

To determine

**To calculate:** The value of

Sect-6.1 P-1CPSect-6.1 P-2CPSect-6.1 P-3CPSect-6.1 P-4CPSect-6.1 P-5CPSect-6.1 P-6CPSect-6.1 P-7CPSect-6.1 P-1SWUSect-6.1 P-2SWUSect-6.1 P-3SWU

Sect-6.1 P-4SWUSect-6.1 P-5SWUSect-6.1 P-6SWUSect-6.1 P-7SWUSect-6.1 P-8SWUSect-6.1 P-9SWUSect-6.1 P-10SWUSect-6.1 P-1ESect-6.1 P-2ESect-6.1 P-3ESect-6.1 P-4ESect-6.1 P-5ESect-6.1 P-6ESect-6.1 P-7ESect-6.1 P-8ESect-6.1 P-9ESect-6.1 P-10ESect-6.1 P-11ESect-6.1 P-12ESect-6.1 P-13ESect-6.1 P-14ESect-6.1 P-15ESect-6.1 P-16ESect-6.1 P-17ESect-6.1 P-18ESect-6.1 P-19ESect-6.1 P-20ESect-6.1 P-21ESect-6.1 P-22ESect-6.1 P-23ESect-6.1 P-24ESect-6.1 P-25ESect-6.1 P-26ESect-6.1 P-27ESect-6.1 P-28ESect-6.1 P-29ESect-6.1 P-30ESect-6.1 P-31ESect-6.1 P-32ESect-6.1 P-33ESect-6.1 P-34ESect-6.1 P-35ESect-6.1 P-36ESect-6.1 P-37ESect-6.1 P-38ESect-6.1 P-39ESect-6.1 P-40ESect-6.1 P-41ESect-6.1 P-42ESect-6.1 P-43ESect-6.1 P-44ESect-6.1 P-45ESect-6.1 P-46ESect-6.1 P-47ESect-6.1 P-48ESect-6.1 P-49ESect-6.1 P-50ESect-6.1 P-51ESect-6.1 P-52ESect-6.1 P-53ESect-6.1 P-54ESect-6.1 P-55ESect-6.1 P-56ESect-6.1 P-57ESect-6.1 P-58ESect-6.1 P-59ESect-6.1 P-60ESect-6.1 P-61ESect-6.1 P-62ESect-6.1 P-63ESect-6.1 P-64ESect-6.1 P-65ESect-6.1 P-66ESect-6.1 P-67ESect-6.1 P-68ESect-6.1 P-69ESect-6.1 P-70ESect-6.1 P-71ESect-6.1 P-72ESect-6.1 P-73ESect-6.1 P-74ESect-6.1 P-75ESect-6.1 P-76ESect-6.1 P-77ESect-6.1 P-78ESect-6.1 P-79ESect-6.1 P-80ESect-6.1 P-81ESect-6.1 P-82ESect-6.2 P-1CPSect-6.2 P-2CPSect-6.2 P-3CPSect-6.2 P-4CPSect-6.2 P-5CPSect-6.2 P-6CPSect-6.2 P-1SWUSect-6.2 P-2SWUSect-6.2 P-3SWUSect-6.2 P-4SWUSect-6.2 P-5SWUSect-6.2 P-6SWUSect-6.2 P-1ESect-6.2 P-2ESect-6.2 P-3ESect-6.2 P-4ESect-6.2 P-5ESect-6.2 P-6ESect-6.2 P-7ESect-6.2 P-8ESect-6.2 P-9ESect-6.2 P-10ESect-6.2 P-11ESect-6.2 P-12ESect-6.2 P-13ESect-6.2 P-14ESect-6.2 P-15ESect-6.2 P-16ESect-6.2 P-17ESect-6.2 P-18ESect-6.2 P-19ESect-6.2 P-20ESect-6.2 P-21ESect-6.2 P-22ESect-6.2 P-23ESect-6.2 P-24ESect-6.2 P-25ESect-6.2 P-26ESect-6.2 P-27ESect-6.2 P-28ESect-6.2 P-29ESect-6.2 P-30ESect-6.2 P-31ESect-6.2 P-32ESect-6.2 P-33ESect-6.2 P-34ESect-6.2 P-35ESect-6.2 P-36ESect-6.2 P-37ESect-6.2 P-38ESect-6.2 P-39ESect-6.2 P-40ESect-6.2 P-41ESect-6.2 P-42ESect-6.2 P-43ESect-6.2 P-44ESect-6.2 P-45ESect-6.2 P-46ESect-6.2 P-47ESect-6.2 P-48ESect-6.2 P-49ESect-6.2 P-50ESect-6.2 P-51ESect-6.2 P-52ESect-6.2 P-53ESect-6.2 P-54ESect-6.2 P-55ESect-6.2 P-56ESect-6.2 P-57ESect-6.2 P-58ESect-6.2 P-59ESect-6.2 P-60ESect-6.2 P-61ESect-6.2 P-1QYSect-6.2 P-2QYSect-6.2 P-3QYSect-6.2 P-4QYSect-6.2 P-5QYSect-6.2 P-6QYSect-6.2 P-7QYSect-6.2 P-8QYSect-6.2 P-9QYSect-6.2 P-10QYSect-6.2 P-11QYSect-6.2 P-12QYSect-6.2 P-13QYSect-6.2 P-14QYSect-6.2 P-15QYSect-6.2 P-16QYSect-6.2 P-17QYSect-6.2 P-18QYSect-6.2 P-19QYSect-6.2 P-20QYSect-6.2 P-21QYSect-6.3 P-1CPSect-6.3 P-2CPSect-6.3 P-3CPSect-6.3 P-1SWUSect-6.3 P-2SWUSect-6.3 P-3SWUSect-6.3 P-4SWUSect-6.3 P-5SWUSect-6.3 P-6SWUSect-6.3 P-7SWUSect-6.3 P-8SWUSect-6.3 P-9SWUSect-6.3 P-10SWUSect-6.3 P-1ESect-6.3 P-2ESect-6.3 P-3ESect-6.3 P-4ESect-6.3 P-5ESect-6.3 P-6ESect-6.3 P-7ESect-6.3 P-8ESect-6.3 P-9ESect-6.3 P-10ESect-6.3 P-11ESect-6.3 P-12ESect-6.3 P-13ESect-6.3 P-14ESect-6.3 P-15ESect-6.3 P-16ESect-6.3 P-17ESect-6.3 P-18ESect-6.3 P-19ESect-6.3 P-20ESect-6.3 P-31ESect-6.3 P-32ESect-6.3 P-33ESect-6.3 P-34ESect-6.3 P-35ESect-6.3 P-36ESect-6.3 P-37ESect-6.3 P-38ESect-6.3 P-39ESect-6.3 P-40ESect-6.3 P-43ESect-6.3 P-44ESect-6.3 P-45ESect-6.3 P-46ESect-6.3 P-47ESect-6.3 P-48ESect-6.4 P-1CPSect-6.4 P-2CPSect-6.4 P-3CPSect-6.4 P-4CPSect-6.4 P-5CPSect-6.4 P-1SWUSect-6.4 P-2SWUSect-6.4 P-3SWUSect-6.4 P-4SWUSect-6.4 P-5SWUSect-6.4 P-6SWUSect-6.4 P-7SWUSect-6.4 P-8SWUSect-6.4 P-9SWUSect-6.4 P-10SWUSect-6.4 P-1ESect-6.4 P-2ESect-6.4 P-3ESect-6.4 P-4ESect-6.4 P-5ESect-6.4 P-6ESect-6.4 P-7ESect-6.4 P-8ESect-6.4 P-9ESect-6.4 P-10ESect-6.4 P-11ESect-6.4 P-12ESect-6.4 P-13ESect-6.4 P-14ESect-6.4 P-15ESect-6.4 P-16ESect-6.4 P-17ESect-6.4 P-18ESect-6.4 P-19ESect-6.4 P-20ESect-6.4 P-21ESect-6.4 P-22ESect-6.4 P-23ESect-6.4 P-24ESect-6.4 P-25ESect-6.4 P-26ESect-6.4 P-27ESect-6.4 P-28ESect-6.4 P-29ESect-6.4 P-30ESect-6.4 P-31ESect-6.4 P-32ESect-6.4 P-33ESect-6.4 P-34ESect-6.4 P-35ESect-6.4 P-36ESect-6.4 P-37ESect-6.4 P-38ESect-6.4 P-39ESect-6.4 P-40ESect-6.4 P-41ESect-6.4 P-42ECh-6 P-1RECh-6 P-2RECh-6 P-3RECh-6 P-4RECh-6 P-5RECh-6 P-6RECh-6 P-7RECh-6 P-8RECh-6 P-9RECh-6 P-10RECh-6 P-11RECh-6 P-12RECh-6 P-13RECh-6 P-14RECh-6 P-15RECh-6 P-16RECh-6 P-17RECh-6 P-18RECh-6 P-19RECh-6 P-20RECh-6 P-21RECh-6 P-22RECh-6 P-23RECh-6 P-24RECh-6 P-25RECh-6 P-26RECh-6 P-27RECh-6 P-28RECh-6 P-29RECh-6 P-30RECh-6 P-31RECh-6 P-32RECh-6 P-33RECh-6 P-34RECh-6 P-35RECh-6 P-36RECh-6 P-37RECh-6 P-38RECh-6 P-39RECh-6 P-40RECh-6 P-41RECh-6 P-42RECh-6 P-43RECh-6 P-44RECh-6 P-45RECh-6 P-46RECh-6 P-47RECh-6 P-48RECh-6 P-49RECh-6 P-50RECh-6 P-51RECh-6 P-52RECh-6 P-53RECh-6 P-54RECh-6 P-55RECh-6 P-56RECh-6 P-57RECh-6 P-58RECh-6 P-59RECh-6 P-60RECh-6 P-61RECh-6 P-62RECh-6 P-63RECh-6 P-64RECh-6 P-1TYSCh-6 P-2TYSCh-6 P-3TYSCh-6 P-4TYSCh-6 P-5TYSCh-6 P-6TYSCh-6 P-7TYSCh-6 P-8TYSCh-6 P-9TYSCh-6 P-10TYSCh-6 P-11TYSCh-6 P-12TYSCh-6 P-13TYSCh-6 P-14TYSCh-6 P-15TYSCh-6 P-16TYSCh-6 P-17TYSCh-6 P-18TYS

Applied Calculus

Single Variable Calculus: Early Transcendentals, Volume I

Precalculus: Mathematics for Calculus (Standalone Book)

Calculus: Early Transcendentals

Finite Mathematics and Applied Calculus (MindTap Course List)

Calculus: Early Transcendental Functions

Multivariable Calculus

Essentials Of Statistics

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

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

Calculus (MindTap Course List)

Understanding Basic Statistics

Statistics for The Behavioral Sciences (MindTap Course List)

Single Variable Calculus

Mathematical Excursions (MindTap Course List)

Finite Mathematics

Mathematical Applications for the Management, Life, and Social Sciences

Probability and Statistics for Engineering and the Sciences

Intermediate Algebra

Single Variable Calculus: Early Transcendentals

Elements Of Modern Algebra

Contemporary Mathematics for Business & Consumers

Elementary Technical Mathematics

Trigonometry (MindTap Course List)

Elementary Geometry For College Students, 7e

Calculus of a Single Variable

Calculus: Early Transcendental Functions (MindTap Course List)

Elementary Geometry for College Students

Finite Mathematics for the Managerial, Life, and Social Sciences

Study Guide for Stewart's Multivariable Calculus, 8th

Multivariable Calculus

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

Research Methods for the Behavioral Sciences (MindTap Course List)

Research Methods for the Behavioral Sciences (MindTap Course List)

STATISTICS F/BUSINESS+ECONOMICS-TEXT

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

College Algebra (MindTap Course List)

Mathematics For Machine Technology

Introduction To Statistics And Data Analysis

Calculus (MindTap Course List)

Mathematics: A Practical Odyssey