5 Steps to a 5 AP Calculus BC 2019

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

Example 2

The graph of a functionfis shown in Figure 13.1-2. Find the average value off on [0, 4].

10

1

2

23 4

y

f

x

Figure 13.1-2

Average value=

1

4 − 0

∫ 4

0

f(x)dx

=

1

4

(

1 + 2 +

3

2

+

3

2

)

=

3

2

.

Example 3

The velocity of a particle moving on a line isv(t)= 3 t^2 − 18 t+24. Find the average velocity

fromt=1tot=3.

Average velocity=

1

3 − 1

∫ 3

1

(3t^2 − 18 t+24)dt

=

1

2

[

t^3 − 9 t^2 + 24 t

] 3

1

=

1

2

[(

33 −9(3^2 )+24(3)

)

−

(

13 −9(1^2 )+24(1)

)]

=

1

2

(18−16)=

1

2

(2)= 1.

Note: The average velocity fort=1tot=3is

s(3)−s(1)

2

, which is equivalent to the

computations above.