Chapter 8.7, Problem 71E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
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=x16âˆ’x2,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=2Ï€âˆ«0axf(x)dx

The integration formula:

âˆ«u2a2âˆ’u2du=18[u(2u2âˆ’a2)a2âˆ’u2+a4arcsinua]

Calculation:

The volume of solid is,

V=2Ï€âˆ«04x(x16âˆ’x2)dx=2Ï€âˆ«04x216âˆ’x2dx

Using the formula, âˆ«u2<

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