   Chapter 5.3, Problem 5E

Chapter
Section
Textbook Problem

# Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the y-axis. y = x 2 ,    0 ≤ x ≤ 2 ,    y = 4 ,    x = 0

To determine

To find:

The volume generated by rotating the region bounded by the given curves about the y-axis using the cylindrical shells.

Explanation

1) Concept:

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

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

V= ab2πxf(x)dx

where  0ab

2) Given:

The region bounded by y=x2, y=4, 0 x2,  x=0 rotated about the y-axis.

3) Calculation:

As the region is the bounded by y=x2, y=4, 0 x2,  x=0 rotated about the y-axis

for shell method, the typical approximating shell with the radius x is

Therefore, the circumference is 2πx and the height is y=4-x2

### 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

#### In Exercises 2528. solve the equation by factoring. 28. 2x4 + x2 = 1

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

#### 60. Write the equation of the line tangent to the curve x at the point where .

Mathematical Applications for the Management, Life, and Social Sciences

#### 0 1 does not exist

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