   Chapter 5.2, Problem 37E

Chapter
Section
Textbook Problem

# Use a computer algebra system to find the exact volume of the solid obtained by rotating the region bounded by the given curves about the specified line. y = sin 2 x ,   y = 0 ,   0 ≤ x ≤ π ;    about y = − 1

To determine

To find:

The exact volume of the solid obtained by rotating the region bounded by the given curves about the line y= -1 by using a computer algebra system.

Explanation

1) Concept:

i. If the cross section is a washer with inner radius rin and outer radius rout, then area of washer is obtained by subtracting the area of the inner disk from the area of the outer disk,

ii. The volume of the solid of revolution about x-axis is

V= abA(x)dx

2) Given:

y=sin2x, y=0, 0xπ; about  y= -1

3) Calculation:

Region bounded by the given curves is shown below:

From the above graph,

x coordinate of the points of intersection: x=0 and  x= π

The cross section is perpendicular to the x-axis, and it is a washer.

Thus, the outer radius is the distance from the curve y=sin2x to the axis of rotation y= -1 and the inner radius is the distance from the line y=0 to the axis of rotation y= -1

### 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

#### Using a binomial series, the Maclaurin series for is:

Study Guide for Stewart's Multivariable Calculus, 8th

#### y=4x2+1 defines y implicitly as a function of x.

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

#### Show that lnex=x

College Algebra (MindTap Course List) 