Using the Trapezoidal Rule and Simpson’s Rule In Exercises 1-10, use the Trapezoidal Rule and Simpson’s Rule to approximate the value of the definite integral for the indicated value of n. Compare these results with the exact value of the definite integral. Round your answers to four decimal places. See Examples 1 and 2.
To calculate: The value of the integral
Given Information:
The definite integral is
Formula used:
1. Trapezoidal Rule:
If a function f is continuous on
2. Simpson’s Rule:
If f is continuous on
Calculation:
Calculation to get exact value:
Consider the definite integral
Simplify as:
Therefore, the exact value:
Calculation by Trapezoidal Rule:
Consider the definite integral
When
And the end points of subintervals are,
For
For
For
For
For
For
For
For
For
By Trapezoidal Rule,
Finite Mathematics and Applied Calculus (MindTap Course List)
Single Variable Calculus: Early Transcendentals, Volume I
Applied Calculus
Precalculus: Mathematics for Calculus (Standalone Book)
Multivariable Calculus
Calculus: Early Transcendental Functions
Calculus: Early Transcendentals
Essentials of Statistics for The Behavioral Sciences (MindTap Course List)
Essentials Of Statistics
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
Finite Mathematics
Mathematical Applications for the Management, Life, and Social Sciences
Mathematical Excursions (MindTap Course List)
Probability and Statistics for Engineering and the Sciences
Intermediate Algebra
Single Variable Calculus: Early Transcendentals
Contemporary Mathematics for Business & Consumers
Elementary Technical Mathematics
Trigonometry (MindTap Course List)
Elementary Geometry For College Students, 7e
Elements Of Modern Algebra
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
Multivariable Calculus
Study Guide for Stewart's Multivariable Calculus, 8th
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)
Introduction To Statistics And Data Analysis
College Algebra (MindTap Course List)
Mathematics For Machine Technology
STATISTICS F/BUSINESS+ECONOMICS-TEXT
Statistics for Business & Economics, Revised (MindTap Course List)