To Find:
To find the area of the given regions by subtracting the area of a triangular region from the area of a larger region on or above the x-axis bounded by the curves
Answer to Problem 35E
The area of the given regions bounded by the curves are
Explanation of Solution
Given information:
The given function is
The red curve is the graph of
Now, we have to find the area by subtracting the triangle formed by
Consider
So the value of y is both positive and negative. However, when we actually solve the equation, only the positive is used because we are trying to find the area above the x-axis.
Therefore, the area of the larger region is
Area of the triangle outside of area that we are trying to find but formed from larger region is
Subtract the area of triangle from area of larger region,
Substitute
When
On Simplifying,
Therefore, the area of the given regions bounded by the curves are
Chapter 8 Solutions
Calculus: Graphical, Numerical, Algebraic
Additional Math Textbook Solutions
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus and Its Applications (11th Edition)
Precalculus Enhanced with Graphing Utilities (7th 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