Concept explainers
To calculate:
The exact area of given function.
Answer to Problem 31E
The exact area of region is
Area |
Explanation of Solution
Given Information:
Function:
Interval:
Sum of Areas of
Area |
Calculation:
To approximate the area of the region for each finite value of
Consider the following function over the interval
Since the interval is
Then, the vertical lines are
Then, the width of each rectangle
And height of each rectangle is
Now, the approximate the area as the sum of the area of
That is,
Then, value of the area for
And the value of the area for
Then, the value of the area for
The value of the area for
The value of the area for
Since,
Then,
Hence the exact area of region is
Therefore, the approximate area of the region bounded by the graph
Area |
Chapter 11 Solutions
Precalculus with Limits: A Graphing Approach
- 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