BuyFindarrow_forward

Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

Solutions

Chapter
Section
BuyFindarrow_forward

Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

The region bounded by the given curves is rotated about the specified axis. Find the volume of the resulting solid by any method.

y 2 x 2 = 1 ,   y = 2 ;    about the  y -axis

To determine

To find:

The volume of the solid obtained by rotating the region bounded by the given curves about the specified line.

Explanation

1) Concept:

The volume of the disk obtained by the revolution about the y-axis is

V= abA(y)dy where A(y) is the area of cross-section perpendicular y-axis.

2) Given:

The region bounded by y2-x2=1, y=2,  rotated about the y- axis.

3) Calculation:

The graph of the region bounded by the given curves is

Find the volume by using the area of disks which are perpendicular to y-axis,

Here, the region is bounded by  y2-x2=1x=±y2-1, y=2

We are interested only in positive y and the region is bounded in y=[1, 2]. So

V=12πy2-12dx

=12π

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started
Sect-5.1 P-11ESect-5.1 P-12ESect-5.1 P-13ESect-5.1 P-14ESect-5.1 P-15ESect-5.1 P-16ESect-5.1 P-17ESect-5.1 P-18ESect-5.1 P-19ESect-5.1 P-20ESect-5.1 P-21ESect-5.1 P-22ESect-5.1 P-23ESect-5.1 P-24ESect-5.1 P-25ESect-5.1 P-26ESect-5.1 P-27ESect-5.1 P-28ESect-5.1 P-29ESect-5.1 P-30ESect-5.1 P-31ESect-5.1 P-32ESect-5.1 P-33ESect-5.1 P-34ESect-5.1 P-35ESect-5.1 P-36ESect-5.1 P-37ESect-5.1 P-38ESect-5.1 P-39ESect-5.1 P-40ESect-5.1 P-41ESect-5.1 P-42ESect-5.1 P-43ESect-5.1 P-44ESect-5.1 P-45ESect-5.1 P-46ESect-5.1 P-47ESect-5.1 P-48ESect-5.1 P-49ESect-5.1 P-50ESect-5.1 P-51ESect-5.1 P-52ESect-5.1 P-53ESect-5.1 P-54ESect-5.1 P-55ESect-5.1 P-56ESect-5.1 P-57ESect-5.1 P-58ESect-5.1 P-59ESect-5.1 P-60ESect-5.1 P-61ESect-5.1 P-62ESect-5.1 P-63ESect-5.1 P-64ESect-5.2 P-1ESect-5.2 P-2ESect-5.2 P-3ESect-5.2 P-4ESect-5.2 P-5ESect-5.2 P-6ESect-5.2 P-7ESect-5.2 P-8ESect-5.2 P-9ESect-5.2 P-10ESect-5.2 P-11ESect-5.2 P-12ESect-5.2 P-13ESect-5.2 P-14ESect-5.2 P-15ESect-5.2 P-16ESect-5.2 P-17ESect-5.2 P-18ESect-5.2 P-19ESect-5.2 P-20ESect-5.2 P-21ESect-5.2 P-22ESect-5.2 P-23ESect-5.2 P-24ESect-5.2 P-25ESect-5.2 P-26ESect-5.2 P-27ESect-5.2 P-28ESect-5.2 P-29ESect-5.2 P-30ESect-5.2 P-31ESect-5.2 P-32ESect-5.2 P-33ESect-5.2 P-34ESect-5.2 P-35ESect-5.2 P-36ESect-5.2 P-37ESect-5.2 P-38ESect-5.2 P-39ESect-5.2 P-40ESect-5.2 P-41ESect-5.2 P-42ESect-5.2 P-43ESect-5.2 P-44ESect-5.2 P-45ESect-5.2 P-46ESect-5.2 P-47ESect-5.2 P-48ESect-5.2 P-49ESect-5.2 P-50ESect-5.2 P-51ESect-5.2 P-52ESect-5.2 P-53ESect-5.2 P-54ESect-5.2 P-55ESect-5.2 P-56ESect-5.2 P-57ESect-5.2 P-58ESect-5.2 P-59ESect-5.2 P-60ESect-5.2 P-61ESect-5.2 P-62ESect-5.2 P-63ESect-5.2 P-64ESect-5.2 P-65ESect-5.2 P-66ESect-5.2 P-67ESect-5.2 P-68ESect-5.2 P-69ESect-5.2 P-70ESect-5.2 P-71ESect-5.2 P-72ESect-5.3 P-1ESect-5.3 P-2ESect-5.3 P-3ESect-5.3 P-4ESect-5.3 P-5ESect-5.3 P-6ESect-5.3 P-7ESect-5.3 P-8ESect-5.3 P-9ESect-5.3 P-10ESect-5.3 P-11ESect-5.3 P-12ESect-5.3 P-13ESect-5.3 P-14ESect-5.3 P-15ESect-5.3 P-16ESect-5.3 P-17ESect-5.3 P-18ESect-5.3 P-19ESect-5.3 P-20ESect-5.3 P-21ESect-5.3 P-22ESect-5.3 P-23ESect-5.3 P-24ESect-5.3 P-25ESect-5.3 P-26ESect-5.3 P-27ESect-5.3 P-28ESect-5.3 P-29ESect-5.3 P-30ESect-5.3 P-31ESect-5.3 P-32ESect-5.3 P-33ESect-5.3 P-34ESect-5.3 P-35ESect-5.3 P-36ESect-5.3 P-37ESect-5.3 P-38ESect-5.3 P-39ESect-5.3 P-40ESect-5.3 P-41ESect-5.3 P-42ESect-5.3 P-43ESect-5.3 P-44ESect-5.3 P-45ESect-5.3 P-46ESect-5.3 P-47ESect-5.3 P-48ESect-5.4 P-1ESect-5.4 P-2ESect-5.4 P-3ESect-5.4 P-4ESect-5.4 P-5ESect-5.4 P-6ESect-5.4 P-7ESect-5.4 P-8ESect-5.4 P-9ESect-5.4 P-10ESect-5.4 P-11ESect-5.4 P-12ESect-5.4 P-13ESect-5.4 P-14ESect-5.4 P-15ESect-5.4 P-16ESect-5.4 P-17ESect-5.4 P-18ESect-5.4 P-19ESect-5.4 P-20ESect-5.4 P-21ESect-5.4 P-22ESect-5.4 P-23ESect-5.4 P-24ESect-5.4 P-25ESect-5.4 P-26ESect-5.4 P-27ESect-5.4 P-28ESect-5.4 P-29ESect-5.4 P-30ESect-5.4 P-31ESect-5.4 P-32ESect-5.4 P-33ESect-5.4 P-34ESect-5.5 P-1ESect-5.5 P-2ESect-5.5 P-3ESect-5.5 P-4ESect-5.5 P-5ESect-5.5 P-6ESect-5.5 P-7ESect-5.5 P-8ESect-5.5 P-9ESect-5.5 P-10ESect-5.5 P-11ESect-5.5 P-12ESect-5.5 P-13ESect-5.5 P-14ESect-5.5 P-15ESect-5.5 P-16ESect-5.5 P-17ESect-5.5 P-18ESect-5.5 P-19ESect-5.5 P-20ESect-5.5 P-21ESect-5.5 P-22ESect-5.5 P-23ESect-5.5 P-24ESect-5.R P-1CCSect-5.R P-2CCSect-5.R P-3CCSect-5.R P-4CCSect-5.R P-5CCSect-5.R P-6CCSect-5.R P-1ESect-5.R P-2ESect-5.R P-3ESect-5.R P-4ESect-5.R P-5ESect-5.R P-6ESect-5.R P-7ESect-5.R P-8ESect-5.R P-9ESect-5.R P-10ESect-5.R P-11ESect-5.R P-12ESect-5.R P-13ESect-5.R P-14ESect-5.R P-15ESect-5.R P-16ESect-5.R P-17ESect-5.R P-18ESect-5.R P-19ESect-5.R P-20ESect-5.R P-21ESect-5.R P-22ESect-5.R P-23ESect-5.R P-24ESect-5.R P-25ESect-5.R P-26ESect-5.R P-27ESect-5.R P-28ESect-5.R P-29ESect-5.R P-30ESect-5.R P-31ESect-5.R P-32ESect-5.R P-33ESect-5.R P-34ESect-5.P P-1PSect-5.P P-2PSect-5.P P-3PSect-5.P P-4PSect-5.P P-5PSect-5.P P-6PSect-5.P P-7PSect-5.P P-8PSect-5.P P-9PSect-5.P P-10PSect-5.P P-11PSect-5.P P-12PSect-5.P P-13PSect-5.P P-14PSect-5.P P-15P

Additional Math Solutions

Find more solutions based on key concepts

Show solutions add

In Exercises 516, evaluate the given quantity. log5125

Finite Mathematics and Applied Calculus (MindTap Course List)

Fill in the blanks. 8. a. The statement limxf(x) = L means that f(x) can be made arbitrarily close to _________...

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

In Problems 23-28, graph the functions.

Mathematical Applications for the Management, Life, and Social Sciences

Convert the following percents to decimals. 13.4%

Contemporary Mathematics for Business & Consumers

True or False: converges conditionally.

Study Guide for Stewart's Multivariable Calculus, 8th

True or False: In the definition of , the expression is interpreted as “the distance between f(x) and L is les...

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Find each product, if possible. [213121010][123221001]

College Algebra (MindTap Course List)

Define the concept of internal validity and a threat to internal validity.

Research Methods for the Behavioral Sciences (MindTap Course List)