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

MA 3972-MA-Book April 11, 2018 16:5

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

Step 5: Substitute initial condition (0, 3) and obtaink=3. Thus, you havey=

3

e

x 22.

3

2

1

• 21 – 1 0 2

y

x

Figure 14.5-7

14.6 Rapid Review

1. Find the average value ofy=sinxon [0,π].

Answer: Average value=

1

π− 0

∫π

0

sinxdx

=

1

π

[

−cosx

]π

0 =

2

π

.

2. Find the total distance traveled by a particle during 0≤t≤3 whose velocity function
   is shown in Figure 14.6-1.
   v

t

v(t)

321

• 1

1

2

Figure 14.6-1

Answer: Total distance traveled=

∫ 2

0

v(t)dt+

∣∣

∣∣

∫ 3

2

v(t)dt

∣∣

∣∣

= 2 + 0. 5 = 2 .5.

3. Oil is leaking from a tank at the rate off(t)= 5 e−^0.^1 tgallons/hour, wheretis measured
   in hours. Write an integral to find the total number of gallons of oil that will have
   leaked from the tank after 10 hours. Do not evaluate the integral.

Answer: Total number of gallons leaked=

∫ 10

0

5 e−^0.^1 tdt.