Concept explainers
To estimate: The
Answer to Problem 8E
The value of the integral
The value of the integral
The value of the integral
Explanation of Solution
Given information:
The function f is an increasing function.
The number of intervals,
Each interval value is
The Riemann sum
The expression to find the integral
Substitute3 for n, 2 for
Substitute
Therefore, the estimation of the integral
For the increasing function of f,the right end points are greater than the exact value of the integral that is overestimate.
The expression to find the integral
Substitute 3 for n,2 for
Substitute
Therefore, the estimation of the integral
For the increasing function of f,the left end points are smaller than the exact value of the integral that is underestimating.
The expression to find the integral
Substitute 3 for n,2 for
Substitute
Therefore, the estimation of the integral
Due to increasing function of f, cannot be concluded about midpoint estimate when compared to the exact value of integral.
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