   Chapter 5.3, Problem 21E

Chapter
Section
Textbook Problem

# (a) Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curve about the specified axis.(b) Use your calculator to evaluate the integral correct to five decimal places. y = sin x ,   y = 0 ,   x = 2 π ,   x = 3 π ;    about the  y -axis

To determine

a)

To find:

The integral for the volume of the solid obtained by rotating the region bounded by the given curve about the specified axis.

Explanation

1) Concept:

i. If x  is the radius of the typical shell, then the circumference =2πx and the height is y=f(x)

ii. By the shell method, the volume of the solid by rotating the region under the curve y=f(x) about x-axis from a to b is

V= ab2πx f(x)dx

Where,  0a<b

2) Given:

y=sinx, y=0, x=2π, x=3π, rotate about y-axis

3) Calculation:

As the region is bounded by y=sinx, y=0, x=2π, x=3π, and rotated about y-axis, draw the region using the given curves

To determine

b)

To evaluate:

The integral ofthe volume of the solid

### 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

#### Expand each expression in Exercises 122. (2xy)y

Finite Mathematics and Applied Calculus (MindTap Course List)

#### In Exercises 1-6, simplify the expression. 3. 12t2+12t+34t21

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

#### True or False: n=1(1)nnn+3 converges.

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