5 Steps to a 5 AP Calculus BC 2019

430 STEP 5. Build Your Test-Taking Confidence

4. The correct answer is shown below.

[−3,3] by [−1,5]

(A) Setx^2 = 4 ⇒x=± 2.

Area ofR=

∫ 2

− 2

(4−x^2 )dx= 4 x−

x^3

3

] 2

− 2

=

(

4(2)−

23

3

)

−

(

4(−2)−

(−2)^3

3

)

=

16

3

−

(

−

16

3

)

=

32

3

.

(B) Sincey=x^2 is an even function,x= 0

dividesRinto two regions of equal area.

Thus,a=0.

(C) AreaR 1 =AreaR 2 =

16

3

.

y

x

y = b

R 1

R 2

y = 4

y = x^2

• √b 0 √b

AreaR 2 =

∫√b

−√b

(b−x^2 )dx

= 2

∫√b

0

(b−x^2 )dx

= 2

[

bx−

x^3

3

]√b

0

= 2

⎡

⎣b

(√

b

)

−

(√

b^3

)

3

⎤

⎦

= 2

(

b^3 /^2 −

b^3 /^2

3

)

= 2

(

2 b^3 /^2

3

)

=

4 b^3 /^2

3

.

Set

4 b^3 /^2

3

=

16

3

⇒b^3 /^2 =4orb= 42 /^3.

(D) Washer Method

V=π

∫ 2

− 2

(4^2 −(x^2 )^2 )dx

=π

∫ 2

− 2

(16−x^4 )dx

=π

[

16 x−

x^5

5

] 2

− 2

=

256 π

5