Concept explainers
To find : The area of the region under the curve and check your answer by sketching the region and using geometry.
Answer to Problem 13E
The area of the region is
Explanation of Solution
Given information:
The given function is
Calculation :
The area A of the region S that lies under the graph of the continuous function is the limit of the sum of the areas of approximating rectangles:
Let
Here,
Width:
Right end point:
Height:
Now, according to definition area is
Now draw the graph of
The shaded region is the required region. Since it a triangle, therefore area is
Hence,
The area of the region is
Chapter 13 Solutions
Precalculus: Mathematics for Calculus - 6th 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