5 Steps to a 5 AP Calculus BC 2019

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

tP. 3 P

(

1 −

P

20

)

yn=yn− 1 +Δx· f′(xn− 1 ,yn− 1 )

0 4 .96 4 +.5(.96)= 4. 48

0.5 4.48 1.042944 4. 48 +.5(1.042944)= 5. 001472

1 5.001472 1.125220 5. 001472 +.5(1.125220)= 5. 564082

1.5 5.564082 1.204839 5. 564082 +.5(1.204839)= 6. 166502

2 6.166502 1.279564 6. 166502 +.5(1.279564)= 6. 806284

2.5 6.806284 1.347002 6. 806284 +.5(1.347002)= 7. 479785

3 7.479785 1.404727 7. 479785 +.5(1.404727)= 8. 182149

3.5 8.182149 1.450431 8. 182149 +.5(1.450431)= 8. 907365

4 8.907365

P(4)≈ 8. 907

13.8 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 13.8-1.
   v

t

v(t)

321

–1

1

2

Figure 13.8-1

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.