5 Steps to a 5 AP Calculus BC 2019

Areas, Volumes, and Arc Lengths 287

Example 2

Using the Washer Method and a calculator, find the volume of the solid generated by
revolving the region in Example 1 about the liney=2.

Step 1. Draw a sketch. (See Figure 12.4-13.)

y = x^3

y = x

y = 2

x

0

y

Figure 12.4-13

Step 2. Determine the outer and inner radii of a washer.
The outer radius=(2−x^3 ) and inner radius=(2−x).

Step 3. Set up an integral.

V=π

∫ 1

0

[(

2 −x^3

) 2

−( 2 −x)^2

]

dx

Step 4. Evaluate the integral.

Enter

∫ (

π∗

(

( 2 −x∧ 3 )∧ 2 −(2−x)∧ 2

)

, x,0,1

)

and obtain

17 π

21

.

The volume of the solid is

17 π

21

.

Example 3

Using the Washer Method and a calculator, find the volume of the solid generated by
revolving the region bounded byy=x^2 andx=y^2 about they-axis.