   Chapter 8.7, Problem 71E

Chapter
Section
Textbook Problem

Volume Consider the region bounded by the graphs of y = x 16 − x 2 ,   y = 0 ,   x = 0 ,   and  x = 4. Find the volume of the solid generated by revolving the region about the y-axis.

To determine

To calculate: The volume of the solid generated by revolving the region bounded by the graphs of y=x16x2,y=0,x=0,x=4 about the y-axis.

Explanation

Given:

The region bounded by the graphs of y=x16x2,y=0,x=0,x=4 is revolved about the y-axis.

Formula used:

The volume of solid of revolution is found by the formula:

V=2π0axf(x)dx

The integration formula:

u2a2u2du=18[u(2u2a2)a2u2+a4arcsinua]

Calculation:

The volume of solid is,

V=2π04x(x16x2)dx=2π04x216x2dx

Using the formula, u2<

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. (2x3)2

Finite Mathematics and Applied Calculus (MindTap Course List)

What is the lowest score in the following distribution?

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

In Problem 18 and 19, determine whether each graph represents as a function of .

Mathematical Applications for the Management, Life, and Social Sciences 