Concept explainers
To approximate:
Answer to Problem 38E
Explanation of Solution
Given information:
Calculation:
Find the width of the intervals:
Calculate f(x) = at the interval boundaries:
x | f(x) |
0 | 1 |
2 | 1 |
4 | 1 |
6 | 1 |
8 | 1 |
10 | 1 |
12 | 1 |
14 | 1 |
16 | 1 |
18 | 1 |
20 | 1 |
Plug everything into the Trapezoid Rule:
Actual value:
Actual value is as expected, even number of parts above and below cancel out to 0.
The interval boundaries just happen to fall on only the peaks, so all the Trapezoids are above the x -axis and the sum will be incorrect. Must use a large n to get a better result.
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