5 Steps to a 5 AP Calculus AB 2019 - William Ma

MA 3972-MA-Book April 11, 2018 16:1

300 STEP 4. Review the Knowledge You Need to Score High

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 13.4-13.)

y = x^3

y = x

y = 2

x

(^01)
y
Figure 13.4-13
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

.

Thus, 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.

Step 1: Draw a sketch. (See Figure 13.4-14.)