302 STEP 4. Review the Knowledge You Need to Score High
- (See Figure 12.9-12.)
y y = x – 2
x = y^2
(4,2)
(1,–1)
x
2
0
–1
Figure 12.9-12
Step 1. Using the Washer Method:
Points of Intersection:
y=x− 2 ⇒x=y+ 2
Sety^2 =y+ 2
⇒y^2 −y− 2 = 0
⇒(y−2)(y+1)= 0
ory=−1ory=2.
Outer radius=y+2;
Inner radius=y^2.
Step 2. V=π
∫ 2
− 1
((
y+ 2
) 2
−
(
y^2
) 2 )
dy
Step 3. Enterπ
∫ (
(y+ 2 )^2
−y∧4, −1, 2)and obtain
72
5
π.
- (See Figure 12.9-13.)
0
(0,8) C
y
x
R 1
2
Figure 12.9-13
Step 1. Using the Washer Method:
y=8, y=x^3
Outer radius =8;
Inner radius =x^3.
V=π
∫ 2
0
(
82 −
(
x^3
) 2 )
dx
Step 2. Enter
∫
π
(
82 −x^6 , x,0,2
)
and obtain
768 π
7
.
- (See Figure 12.9-14.)
8
y
B (2,8)
R 2
0 A (2,0) x
Figure 12.9-14