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8th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781305270336

Chapter 6.3, Problem 38E

Textbook Problem

The region bounded by the given curves is rotated about the specified axis. Find the volume of the resulting solid by any method.

*y* = −*x*^{2} + 6*x* − 8, *y* = 0; about the *x*-axis

Expert Solution

To determine

**To find:** The volume of the resulting solid by the region bounded by given curve using the method of disk.

**Given:**

The equation about the *x*-axis is

**Calculation:**

Show the equation as below:

Plot a graph for the equation

Calculate *y* value using Equation (1)

Substitute 0 for *x* in Equation (1).

Hence, the co-ordinate of

Calculate *y* value using Equation (1).

Substitute 1 for *x* in Equation (1).

Hence, the co-ordinate of

Calculate *y* value using Equation (1).

Substitute 2 for *x* in Equation (1).

The co-ordinate of

Calculate *y* value using Equation (1)

Substitute 3 for *x* in Equation (1).

The co-ordinate of

Calculate *y* value using Equation (1)

Substitute 4 for *x* in Equation (1).

The co-ordinate of

Draw the disk as shown in Figure 1.

Calculate the volume using the method of disk:

Substitute 2 for *a*, 4 for *b*, and

Single Variable Calculus: Early Transcendentals

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