Concept explainers
a.
To estimate: the x -coordinates of the points of intersection of the curves.
a.
Answer to Problem 16RE
x −coordinates of the points of intersection are 0 and 0.699.
Explanation of Solution
Given information: Let R be the region bounded by curves
Calculation:
By using graphing utility, the graph of the curves
From the graph, the x −coordinates of the points of intersection are 0 and 0.699.
b.
To estimate: the area of R .
b.
Answer to Problem 16RE
Explanation of Solution
Given information: Let R be the region bounded by curves
Calculation:
Find the limits of the
To find the other root use a graphing system , second root is:
Solve the integral for Area:
c.
To estimate: the volume generated when R is rotated about the x -axis.
c.
Answer to Problem 16RE
Explanation of Solution
Given information: Let R be the region bounded by curves
Calculation:
Find the limits of the integration by solving the system of equations:
To find the other root use a graphing system, second root is:
Now, solve the integral for the Area:
Now let’s find the Area, the cross section of the Solid in respect to x is the difference :
Between the outer circle
d.
To estimate: the volume generated when R is rotated about the y -axis.
d.
Answer to Problem 16RE
Explanation of Solution
Given information: Let R be the region bounded by curves
Calculation:
Find the limits of the integration by solving the system of equations:
To find the other root use a graphing system, second root is:
The volume of a solid obtained by rotating about the y −axis the region under the curve.
Chapter 6 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced 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