5 Steps to a 5 AP Calculus BC 2019

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

15. (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.

16. (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

.

17. (See Figure 12.9-14.)

8

y

B (2,8)

R 2

0 A (2,0) x

Figure 12.9-14