To find:The volume of the solid generated by resolving the region bounded by the curves.
Answer to Problem 48RE
The volume of the solid generated is
Explanation of Solution
Given information:
Formula used:
The formula for cylindrical shell is,
Calculation:
Let's graph thegiven area and draw some conclusions based on it.
From the graph, it is noted that the point of intersection is
The distance from the
Thus, the height of the strip is the difference between the graphs.
Substituting the value of
The above integral is evaluated by dividing into two integral,
Where,
Let’s take,
Solving the integrals by using the formula,
Thus,
Let’s take,
Thus,
Now, adding both the integrals to get the volume of the solid,
Therefore, the volume of the solid generated is
Chapter 7 Solutions
Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020
- 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