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

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

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

Step 1: x^2 +y^2 = 4 ⇒y^2 = 4 −x^2 ⇒

y=±

√

4 −x^2

Lets=a side of an equilateral

triangle

s= 2

√

4 −x^2.

Step 2: Area of a cross section:

A(x)=

s^2

√

3

4

=

(

2

√

4 −x^2

) 2 √

3

4

.

Step 3: V=

∫ 2

− 2

(

2

√

4 −x^2

) 2

√

3

4

dx

=

∫ 2

− 2

√

3(4−x^2 )dx

Step 4: Enter

∫ (√

(3)∗(4−x^2 ),x, −2, 2

)

and obtain

32

√

3

3

.

15. (See Figure 13.8-12.)

y

y = x – 2

x = y^2

(4, 2)

(1, –1)

x

2

0

• 1

Figure 13.8-12

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: Enter

π

∫ (

(y+ 2 )∧ 2 −y∧4,−1, 2)

and obtain

72

5

π.

16. (See Figure 13.8-13.)

0

(0, 8) C

y

x

R 1

2

Figure 13.8-13

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

.