To check: If the given sum is an overestimate or underestimate for the actual length of the curve.
Answer to Problem 6RWDT
The given sum is an underestimate for the actual length of the curve.
Explanation of Solution
Given information:
The sum
The figure shows the segment approximating the arc above the subinterval
The length of the segment is
This sum approximates the length of the curve.
Since it is the sum of the shortest distances between the starting and the ending point of the sections of the original curve.
It clearly suggests that it is an underestimate for the length of curve.
Thus,
Chapter 7 Solutions
CALCULUS:GRAPHICAL,...,AP ED.-W/ACCESS
- 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