Concept explainers
To explain: whether the midpoint Rule is always more accurate than the Trapezoidal Rule
Answer to Problem 16RQ
The accuracy of the different approximation methods always depends on the function being approximated
Explanation of Solution
Given information: We have been given Midpoint Rule and Trapezoidal Rule
The midpoint rule approximates the definite integral using rectangular regions whereas
the trapezoidal rule approximates the definite integral using trapezoidal approximations
one rule works better then the other rule. The accuracy of the Rule always depends on the function being
Approximated. For example, make a function which is linear except it has narrow spikes at the mid points of the
Subdivided Intervals. Then the approximating rectangles for the Midpoint Rule will rise up to the level of the spikes,
And be a huge overestimate.
The Trapezoidal Rule basically not count the spikes.
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