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

MA 3972-MA-Book April 11, 2018 12:11

Take a Diagnostic Exam 23

35. If f′(x)=g(x) andgis a continuous function
    for all real values ofx, then

∫ 2

0

g(3x)dxis

(A)

1

3

f(6)−

1

3

f(0).

(B) f(2)− f(0).

(C) f(6)−f(0).

(D)

1

3

f(0)−

1

3

f(6).

36. Evaluate

∫x

π

sin (2t)dt.

37. If a function fis continuous for all values of
    x, which of the following statements is/are
    always true?

I.

∫c

a

f(x)dx=

∫b

a

f(x)dx

+

∫c

b

f(x)dx

II.

∫b

a

f(x)dx=

∫c

a

f(x)dx

−

∫b

c

f(x)dx

III.

∫c

b

f(x)dx=

∫a

b

f(x)dx

−

∫a

c

f(x)dx

38. Ifg(x)=

∫x

π/ 2

2 sintdton

[

π

2

,

5 π

2

]

, find

the value(s) ofxwhereghas a local

minimum.

Chapter 13

39. The graph of the velocity function of a
    moving particle is shown in the following
    figure. What is the total distance traveled by
    the particle during 0≤t≤6?

0

10

− 10

20

2468

v

v(t)

(feet/second)

t

(seconds)

40. The graph of fconsists of four line segments,
    for− 1 ≤x≤5 as shown in the figure below.
    What is the value of

∫ 5

− 1

f(x)dx?

y

f

x

− 1

− 1

1

012345

41. Find the area of the region enclosed by the
    graph ofy=x^2 −xand thex-axis.


42. If

∫k

−k

f(x)dx=0 for all real values ofk, then

which of the graphs shown on the next page

could be the graph of f?

43. The area under the curvey=

√

xfromx= 1

tox=kis 8. Find the value ofk.

44. For 0≤x≤ 3 π, find the area of the region
    bounded by the graphs ofy=sinxand
    y=cosx.


45. Let f be a continuous function on [0, 6] that
    has selected values as shown below:

x 0123456

f(x)12510172637