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

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

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

Area of RectII = f(6)Δx 2 =(3.61)(4)= 14. 44.

Area of RectIII=f(10)Δx 3 =(4.58)(4)= 18. 32.

Total Area= 8. 96 + 14. 44 + 18. 32 = 41. 72.

The area under the curve is approximately

41.72.

13.9 Solutions to Cumulative Review Problems

21. (See Figure 13.9-1.)

[–3, 3] by [–1, 7]

Figure 13.9-1

∫a

−a

ex

2

dx=

∫ 0

−a

ex

2

dx+

∫a

0

ex

2

dx

Sinceex^2 is an even function, thus

∫ 0

−a

ex^2 dx=

∫a

0

ex^2 dx.

k= 2

∫a

0

ex

2

dxand

∫a

0

ex

2

dx=

k

2

.

22. (See Figure 13.9-2.)

9

x

y

θ

Figure 13.9-2

sinθ=

9

x

Differentiate both sides:

cosθ

dθ

dt

=(9)(−x−^2 )

dx

dt

.

Whenx=15, 9^2 +y^2 = 152 ⇒ y= 12.

Thus, cosθ=

12

15

=

4

5

;

dx

dt

=−2 ft/sec.

4

5

dθ

dt

= 9

(

−

1

152

)

(−2)

=

dθ

dt

=

18

152

5

4

=

1

10

radian/sec.

23. (See Figure 13.9-3.)

[–2, 5] by [–2, 6]

Figure 13.9-3

Step 1: Distance Formula:

L=

√

(x− 4 )^2 +(y− 1 )^2

=

√

(x− 4 )^2 +

(

x^2

2

− 1

) 2

where the domain is all real

numbers.

Step 2: Entery 1 =

√

((x−4)∧ 2 +(. 5 x∧ 2 −1)∧2)

Entery 2 =d

(

y 1 (x),x

)

.