Concept explainers
a.
To calculate: The
a.
Answer to Problem 47RE
The integral value of the integral is
Therefore, the answers of the integral are overestimates.
Explanation of Solution
Given information:
The given expression is
Formula used:
Assume that f(x) is continuous on [a, b].
Let n be a positive Integer and
If [a, b] is divided into n sub intervals, each of length
Calculation:
Each subinterval has length
0 | |
0.1 | |
0.2 | |
0.3 | |
0.4 | |
0.5 | |
0.6 | |
0.7 | |
0.8 | |
0.9 | |
1 |
The integral can be obtained as,
b.
To calculate: The integral value by using Midpoint Rule.
b.
Answer to Problem 47RE
The integral value of the integral is
Therefore, the answers of the integral are overestimates.
Explanation of Solution
Given information:
The given expression is
Formula used:
Assume that f(x) is continuous on [a, b].
Let n be a positive Integer and
If [a, b] is divided into n sub intervals, each of length
Calculation: Each subinterval has length
0 | |
0.1 | |
0.2 | |
0.3 | |
0.4 | |
0.5 | |
0.6 | |
0.7 | |
0.8 | |
0.9 | |
1 |
The integral value of the given integral can be obtained as,
c.
To calculate: The integral value by using Simpson’s Rule.
c.
Answer to Problem 47RE
The integral value of the integral is
Therefore, the answers of the integral are overestimates.
Explanation of Solution
Given information:
The given expression is
Formula used:
Assume that f(x) is continuous on [a, b].
Let n be a positive Integer and
If [a, b] is divided into n sub intervals, each of length
Calculation:
Each subinterval has length
0 | |
0.1 | |
0.2 | |
0.3 | |
0.4 | |
0.5 | |
0.6 | |
0.7 | |
0.8 | |
0.9 | |
1 |
The integral can be obtained as,
Chapter 5 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning