Name:
Date:
Block:
Integration Revision 2
Multiple Choice – Calculator Active
1) If

25
10
f ( x)dx  A and

50
25

50
10
(B) A – B
(A) A + B
2)
f ( x)dx  B , then
f ( x)dx 
(C) 0
d x2 2
sin t dt =
dx 0
(A) x 2sin 2  x 2 
(D) x 2 cos 2  x 2 
(B) 2 xsin 2  x 2 
(E) 2 x cos 2  x 2 
(C) sin 2  x 2 
3) Approximate
1
 sin
0
2
xdx using the Trapezoidal Rule with n = 4.
(A) 0.277
(D) 1.109
(B) 0.273
(E) 2.219
(C) 0.555
4)

sec3 x tan x
dx =
1  tan 2 x
1
sec 4 x  C
4
1
(B) sec 2 x  C
2
1
(C) sec 2 x tan 2 x  C
4
(A)
5)
(D) sec x  C
(E) None of these
d 4x
tan t dt 
dx 3 x
(A) tan 4x  tan3x
(B) sec2 4 x  sec 2 3 x
(C) 4 tan 4x  3tan 3x
(D) 4sec2 4 x  3sec 2 3 x
1
1
(E) tan 4 x  tan 3 x
4
3
(D) B – A
(E) 40
Free Response – Non-Calculator
1) The figure below shows the graph of g(x), where g is the derivative of the function f, for 3  x  9 . The
graph consists of three semicircular regions and has horizontal tangent lines at x  0, x  4.5 , and x  7.5 .
a) Find all values of x , for 3  x  9 , at which f attains a relative minimum. Justify your
answer.
b) Find all values of x , for 3  x  9 , at which f attains a relative maximum. Justify your
answer.
x
c) If f ( x)   g (t )dt , find f (6)
3
d) Find all points where f ( x)  0. Justify your answer.
2) Three trains, A, B, and C each travel on a straight track for 0  t  16 hours. The graphs below, which
consist of line segments, show the velocities, in kilometers per hour, of trains A and B. The velocity of
train C is given by the equation v(t )  8t  0.25t 2 .
a) Find the velocities of trains A and C at time t = 6 hours.
b) Find the accelerations of trains B and C at time t = 6 hours.
c) Find the positive difference between the total distance that A traveled and the total distance
that B traveled in 16 hours.
d) Find the total distance that C traveled in 16 hours.
Free Response – Calculator Active
H
3) The temperature on New Year’s Day in Freezton was given by the equation T ( H )   A  B cos 
 12
where T is the temperature in degrees Fahrenheit and H is the number of hours from
midnight (0  H  24) .
a) The initial temperature at midnight was 15 F, and at Noon of New Year’s Day was 5 F.
A and B.

,

Find
b) Find the average temperature for the first 10 hours.
c) Use the Trapezoidal Rule with 4 equal subdivisions to estimate
8
 T (H )dH . Show your Riemann
6
Sum and explain the meaning of your answer.
d) Find an expression for the rate that the temperature is changing with respect to H.
4) A particle moves along the x-axis so that its acceleration at any time t > 0 is given by the equation
a(t )  12t  18 . At time t  1, the velocity of the particle is v 1  0 and the position is x 1  9 .
a) Write an expression for the velocity of the particle v (t ) .
b) At what values of t does the particle change direction?
c) Write an expression for the position x(t ) of the particle.
d) Find the total distance traveled by the particle from t 
3
to t  6 .
2
1)
2)
3)
4)