Practice Integration Problems #2 Name:______________________________

y
1) The figure to the right shows the graph of the velocity of a particle
moving along the x-axis as a function of time. If the particle is at the A B
origin when t = 0, then which of the marked points is the particle C t
furthest from the origin? E

(A) A (B) B (C) C

(D) D (E) E D


2) sin(3x  4)dx 

1
(A)  cos(3x  4)  C (B)  cos(3x  4)  C (C) 3cos(3x  4)  C
3

1
(D) cos(3x  4)  C (E) cos(3x  4)  C
3

x, x  0 1
3) Let f(x) be the function defined by f(x) =
x  1, x > 0
. The value of  xf ( x)dx 
2

(A) 3/2
(B) 5/2
(C) 3
(D) 7/2
(E) 11/2

1 
4) The average value of the function f(x) = cos  x  on the closed interval [-4, 0] is
2 

(A) -1/2sin(2) (B) -1/4sin(2) (C) 1/2cos(2) (D) 1/4sin(2) (E) 1/2sin(2)
5) Let R(t) represent the rate at which water is leaking out of a tank, where t is measured in hours. Which of the
following expressions represents the total amount of water in gallons that leaks out in the first three hours?

R(3)  R(0)
3 3 3
1
(A) R(3) – R(0) (B)
30
(C)  R(t )dt
0
(D)  R '(t )dt
0
(E)
3 0
R(t )dt

1 7 1
6) Suppose that f(x) is an even function and let 
0
f ( x)dx = 5 and 
0
f ( x)dx = 1. What is  f ( x)dx ?
7

(A) – 5
(B) -4
(C) 0
(D) 4
(E) 5

7) As shown in the figure to the right, the function f(x) consists of

(A) 2
(B) 3.714
(C) 3.9
(D) 22.283
(E) 41.144

8) If f is the function defined by f(x) = 3

(A) –3.882
(B) –3.557
(C) 1.710
(D) 3.557
(E) 3.882

9) If f and g are continuously differentiable functions defined for all real numbers, which of the following definite
integrals is equal to f(g(4)) – f(g(2))?

4 4 4
(A) 
2
f '( g ( x))dx (B) 
2
f ( g ( x)) f '( x)dx (C)  f ( g ( x)) g '( x)dx
2
4 4
(D)  f '( g ( x)) g '( x)dx
2
(E)  f '( g '( x)) g '( x)dx
2
 x 1
5
10) If the substitution u = x  1 is made, the integral 2
x
dx =

5 2 2
2u 2 u2 u2
(A) 2 u 2  1 du (B) 1 u 2  1 du (C) 1 2(u 2  1) du

5 2
u 2u 2
(D)  2 du (E) 1 u 2  1 du
2
u 1

 (2 x  kx 2  2k )dx  12 , then k must be

(A) -3
(B) -2
(C) 1
(D) 2
(E) 3

x3
d
12) 
dx x
sin(t 2 ) dt 

(A) sin(x6) – sin(x2) (B) 6x2sin(x3) – 2sin(x) (C) 3x2sin(x6) – sin(x2)

(D) 6x5sin(x6) – 2sin(x2) (E) 2x3cos(x6) –2 cos(x2)