Concept explainers
To find: Approximating the area of region using the indicated numbers
Answer to Problem 28E
Approximating the area of region with the number n of rectangles is
n | 4 | 8 | 20 | 50 |
Approximate area | 5.15625 | 5.5078125 | 5.78625 | 5.9118 |
Explanation of Solution
Given information:
The given function is,
And, rectangles are
Concept used:
The area of a region;
Let
The given function is,
The area of the region bounded by the graph of
The dimensions of the rectangles;
And,
Given function;
Approximate the areas as the sum of the areas of
Now,
We can obtain a more accurate approximation of the area of the region by increasing the number of rectangles.
Take,
In this way, we take
Now, values of
Finally,to approximating the area of region by using values in the following table.
n | 4 | 8 | 20 | 50 |
Approximate area | 5.15625 | 5.5078125 | 5.78625 | 5.9118 |
Chapter 12 Solutions
EBK PRECALCULUS W/LIMITS
- 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