Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use the numeric integration feature on your calculator to find the integral.
1)
3
1ln (t) dt
1)
A)
2.29584
B)
1.29584
C)
0.29584
D)
None of the above
Provide the proper response.
2)
If we decide to use the substitution u = x2+ e, then which of the following might be necessary?
i) du = 2x dx
ii) x2= u – e
iii) du = 2ex dx
iv) du =2x
3 dx
2)
A)
Only i
B)
Both i and iv
C)
Both ii and iii
D)
Both i and ii
Evaluate the indefinite integral.
3)
x4(x4+12x –7) dx
3)
A)
x5
5x4+12x –7+x4x5
5+6x2–7x + C
B)
x9
9+ 2x6–7x5
5+ C
C)
x9
9+6x2–7x + C
D)
x5
5x5
5+6x2–7x + C
4)
4)
A)
Rate of change of population
B)
Total increase in population
C)
Total time elapsed
D)
Total number of births
Approximate the area under the graph of f(x) over the specified interval by dividing the interval into the indicated
number of subintervals and using the left endpoint of each subinterval.
5)
f(x) = 0.1x4–x2+ 3; interval [0, 4]; 4 subintervals
5)
A)
7.8
B)
20.4
C)
17.4
D)
35.8
Find the integral.
6)
4
0x4ln 2x dx
6)
A)
391.74
B)
–202.72
C)
384.91
D)
466.83
7)
7
0xe– x dx
7)
A)
–6e–7+ 1
B)
–8e–7+ 1
C)
–8e–7– 1
D)
–8e–7
8)
3
0(x + 5) ln x dx
8)
A)
2.69
B)
4.17
C)
–2.15
D)
17.69
9)
364x5dx
9)
A)
32
3x8/3 + C
B)
20
3x3/3 + C
C)
3
2x8/3 + C
D)
2
3x6+ C
10)
x2
4x3+ 3 dx
10)
A)
12 ln(4x3+ 3) + C
B)
1
12 ln 4x3+ 3 + C
C)
1
4 ln 4x3+ 3 + C
D)
12 ln 4x3+ 3 + C
11)
9x2+54 dx
11)
A)
3
2x x2+6+6 ln x +x2+6+ C
B)
3
2x x2+54 +54 ln x +x2+54 + C
C)
1
2x 9x2+54 +54 ln x +9x2+54 + C
D)
1
2x x2+6+6 ln x +x2+6+ C
12)
3
0(x3– 4x) dx
12)
A)
12,206.25; the shaded area above the x–axis minus the shaded area below the x–axis is equal
to 12,206.25.
B)
10.25; the total shaded area is equal to 10.25
C)
12,206.25; the total shaded area is equal to 12,206.25.
D)
10.25; the shaded area above the x–axis minus the shaded area below the x–axis is equal to
10.25.
13)
A manufacturer determined that its marginal cost per unit produced is given by the function
C'(x) = 0.0006x2– 0.4x +87.
Find the total cost of producing the 401st unit through the 500th unit.
13)
A)
$2900
B)
$2876.96
C)
$15,100
D)
$9000
14)
y = x, y = x2
14)
A)
1
12
B)
1
3
C)
1
6
D)
1
2
15)
Satterfield Pavement’s marginal cost, in dollars, of paving a road with asphalt is given by
C'(x) =3
8x2–25x +2200, for x 20,
where x is measured in hundreds of feet. Use 4 subintervals over [0, 10] and the left endpoint of
each subinterval to approximate the total cost of paving 1000 feet of road.
15)
A)
$21,076.56
B)
$8457.81
C)
$21,144.53
D)
$23,019.53
16)
y =ex; [1, 2]
16)
A)
e2+ e
B)
e2– e
C)
e2+ e – 1
D)
e2– e + 1
17)
y =9
x; [1, 8]
17)
A)
ln 8
B)
ln 72
C)
8 ln 9
D)
9 ln 8
18)
x = 0, x = 1, y = x2+ 6, y = x2+ 2
18)
A)
8
B)
16
C)
4
D)
12
Evaluate.
19)
1
0
13
8x2dx
19)
A)
13
4
B)
13
24
C)
–13
24
D)
13
8
20)
5
0x3– 1 dx
20)
A)
–639
4
B)
651
4
C)
309
2
D)
611
4
21)
ln x
x(7+ ln x) dx
21)
A)
ln (x) – 7 ln (ln (x) + 7) + C
B)
7 ln (ln (x) + 7) + C
C)
ln (ln (x) + 7) + C
D)
ln (x) + x + 7 ln (ln (x) + 7) + C
22)
x +6
x +3 dx
22)
A)
–3
(x +3)2+ C
B)
x +9 ln x +3+ C
C)
x +3 ln x +3+ C
D)
(x2/2 +6x) ln x +3+ C
23)
1
–18x –3 dx
23)
A)
61
8
B)
73
C)
55
8
D)
73
8
24)
A particle moves so that its velocity (in m/s) is given by v = 2te–t, where t is the time (in seconds).
Find the distance traveled between t = 0 and t =5.
24)
A)
0.38
B)
2.05
C)
1.92
D)
8.14
25)
The time required for workers to produce each unit of a product decreases as the workers become
more familiar with the production procedure. It is determined that the function for the learning
process is
T(x) = 2 + 0.3 1
x ,
where T(x) is the time, in hours, required to produce the xth unit. Find the time required for a new
worker to produce units 10 through 19.
25)
A)
38.88 hr
B)
–0.81 hr
C)
18.19 hr
D)
36.88 hr
26)
4
0x –3 dx
26)
A)
13
2
B)
3
2
C)
11
D)
5
27)
2
1
t8–t4
t6dx
27)
A)
9
2
B)
11
6
C)
5
6
D)
19
6
28)
The rate at which an assembly line worker’s efficiency E (expressed as a percent) changes with
respect to time t is given by E'(t) =75 –6t, where t is the number of hours since the worker’s shift
began. Assuming that E(1) =92, find E(t).
28)
A)
E(t) =75t –6t2+20
B)
E(t) =75t –3t2+92
C)
E(t) =75t –3t2+164
D)
E(t) =75t –3t2+20
29)
If r(t) is the rate of change of sales, then b
ar(t) dt is
i) the total sales up to time b.
ii) the total sales from time a to time b.
iii) the change in sales at any time.
29)
A)
Only ii is correct.
B)
Only i is correct.
C)
Only iii is correct.
D)
Both i and ii could be correct.
30)
(t –4)3 dt
30)
A)
t4
4–64t + C
B)
3t2–24t +48 + C
C)
t4
4–4t3+24t2–64t + C
D)
t4–12t3+48t2–64t + C
31)
t2–9
t –3dt
31)
A)
t2+3t + C
B)
t2
2+3t + C
C)
t2
2+ C
D)
1
32)
32)
A)
Rate of change of cost
B)
Total cost
C)
Cost per unit
D)
Total number of units
33)
Given the rate of change f'(x) of a quantity f(x), b
af'(x) dx represents
i) the total change of f(x) between y = a and y = b.
ii) the total change of f(x) between x = a and x = b.
iii) the partial change of f(x) between x = a and x = b.
33)
A)
Both i and ii could be correct.
B)
Only ii is correct.
C)
Only iii is correct.
D)
Only i is correct.
34)
f'(x) = x –4, f(1) =5
34)
A)
f(x) =x2
2–4x +17
2
B)
f(x) =x2–4x +8
C)
f(x) =x2
2–4x +19
2
D)
f(x) =x2–4x
35)
ln x7
x dx
35)
A)
1
ln x7+ C
B)
1
7(ln x7)2+ C
C)
1
2(ln x7)2+ C
D)
1
14(ln x7)2+ C
36)
y =3x5 ; [–2, 2]
36)
A)
8
B)
16
C)
64
D)
0
37)
(2x5– 7x3+ 6) dx
37)
A)
6x6–7
3 x4+ 6x + C
B)
1
3 x6–7
4 x4+ 6x + C
C)
1
2 x6–7
3 x4+ 6x + C
D)
6x6–7
4 x4+ 6x + C
Find the area under the graph of the function over the interval given.
38)
y = 2x + 7; [1, 5]
38)
A)
52
B)
9
C)
26
D)
18
11
39)
ln 9x dx
39)
A)
9x ln x – x + C
B)
x ln 9x – 9x + C
C)
x ln 9x – x + C
D)
x ln 9x + x + C
40)
b
05e–5x dx
40)
A)
e–5b – 1
B)
1 –e–5b
C)
5–5e–5b
D)
–e–5b
41)
1
x25 +x2dx
41)
A)
–1
5 ln 5+25 –x2
x+ C
B)
1
5 ln 5+25 +x2
x+ C
C)
ln x +x2+25 + C
D)
–1
5 ln 5+25 +x2
x+ C
42)
5x3 ln x dx
42)
A)
x4ln x
4–1
16 + C
B)
5x ln x –5x + C
C)
x4
5ln x
4–1
16 + C
D)
5x4ln x
4–1
16 + C
43)
3
0(x –3)2 dx
43)
A)
0
B)
9
C)
– 3
D)
27
44)
y = –x2+ 9; [0, 3]
44)
A)
36
B)
0
C)
27
D)
18
45)
In defining the definite integral for f(x) on the interval [a,b], we compute x =(b – a)
n. If the
integral is being used to define area under a curve, then what does x represent?
45)
A)
It represents the height of the rectangle used to approximate the area.
B)
It represents the width of the rectangles used to approximate the area.
C)
It represents the width of the single rectangle used to approximate the area.
D)
None of the above
46)
ex
e2x – 9 dx
46)
A)
1
6 ln e2x – 3
e2x + 3 + C
B)
1
18 ln ex– ln 3
ex+ ln 3+ C
C)
1
3 ln ex– 3
ex+ 3 + C
D)
1
6 ln 3–ex
ex+ 3 + C
47)
7x6
(6 +x7)3 dx
47)
A)
–7x6
(6 +x7)2+ C
B)
–1
4(6 +x7)4+ C
C)
–1
2(6 +x7)2+ C
D)
1
4(6 +x7)4+ C
48)
x 6 – x dx
48)
A)
–2
3x(6 – x)3/2 –2
5(6 – x)5/2 + C
B)
–2
3x(6 – x)3/2 +4
15(6 – x)5/2 + C
C)
2
3x(6 – x)3/2 +4
15(6 – x)5/2 + C
D)
–2
3x(6 – x)3/2 –4
15(6 – x)5/2 + C
49)
1
0
x
x + 1 dx
49)
A)
–0.94
B)
0.39
C)
–2.27
D)
–1.33
50)
The rate of growth of a microbe population is given by m'(x) = 30xe2x,where x is time in days.
What is the change in population in the first 3 days?
50)
A)
30,272
B)
15,136
C)
60,544
D)
15,129
51)
A company finds that its marginal revenue from the sale of the xth unit of its product is given by
R'(x) =7x2–4. Assuming that R(0) = 0, find the total–revenue function R.
51)
A)
R(x) =7
3x3–2x
B)
R(x) =14x
C)
R(x) =7
3x3–4x
D)
R(x) =7
2x3–4x2
52)
te–7t2 dt
52)
A)
–1
14 e–7t2+ C
B)
–1
7e–7t2+ C
C)
1
7e–7t2+ C
D)
1
14 e–7t2+ C
53)
Which integral has a value of zero?
i) b
br(t) dt ii) b
–bt3 dt
iii) b
0t3 dt , where b > 0 iv) 10
bt3 dt , where b < 0
53)
A)
Both i and ii
B)
Only iv
C)
Only iii
D)
All of these
54)
f(x) = 0.2x3+ 0.3x2– 0.5x – 1; interval [2, 5]; 3 subintervals
54)
A)
21.0
B)
50.0
C)
49.2
D)
30.0
15
55)
If r(t) is the rate of change of revenue, then b
ar(t) dt is
i) the total revenue up to time b.
ii) the total revenue from time a to time b.
iii) the change in revenue at any time.
55)
A)
Only i is correct.
B)
Only ii is correct.
C)
Only iii is correct.
D)
Both i and ii could be correct.
56)
x6 x7+9 dx
56)
A)
1
14 x7+9+ C
B)
2
3(x7+9)3/2 + C
C)
2
21(x7+9)3/2 + C
D)
2
21x7(x7+9)3/2 + C
57)
9
4
t2+ 1
t dt
57)
A)
212
B)
447
5
C)
472
5
D)
432
5
Write summation notation for the expression.
58)
7+14 +21 +28 +35
58)
A)
35
i=7i
B)
5
i=17i
C)
7
i=15i
D)
35
i=77i
59)
(7 + t) t dt
59)
A)
14
3t3/2 +2
5t5/2 + C
B)
7t3/2 +t5/2 + C
C)
14
3t3/2 +1
2t2+ C
D)
21
2t3/2 +5
2t5/2 + C
60)
The area under the graph of f over the interval [–2, 2]
f(x) =5–x2,if x < 0,
5, if x 0
60)
A)
44
3
B)
52
3
C)
12
D)
8
3
61)
y = x3, y = 4x
61)
A)
2
B)
16
C)
8
D)
4
Solve the problem.
62)
The rate of growth of profit (in millions) from an invention is approximated by P'(x) = xe–x2, where
x represents time in years. The total profit in year 2 that the invention is in operation is $15,000.
Find the total profit function P(x).
62)
A)
P(x) = – 1
2e–x2– 24,000
B)
P(x) = –0.5e–x2+ 0.024
C)
P(x) = – 1
2e–x2– 0.024
D)
P(x) = –0.5e–x2+ 24,000
63)
Find the area of the region bounded by y =x3–27x +5, the x–axis, and the first coordinates of the
relative maximum and minimum values of the function.
63)
A)
30
B)
15
C)
–345
2
D)
–294
Solve the problem.
64)
The rate of water usage for a business, in gallons per day, is given by W(t) =621te–t, where t = the
number of hours since midnight. Approximately how many gallons of water does the business use
in the first 6 hours of the day?
64)
A)
11 gallons
B)
610 gallons
C)
632 gallons
D)
613 gallons
65)
The flow of blood in a blood vessel is faster toward the center of the vessel and slower toward the
outside. The speed of the blood is given by
V =p
4Lv(R2–r2),
where R is the radius of the blood vessel, r is the distance of the blood from the center of the vessel,
and p, v, and L are physical constants related to the pressure and viscosity of the blood and the
length of the blood vessel. If R is constant, we can think of V as a function of r:
V(r) =p
4Lv(R2–r2).
The total blood flow, Q, is given by
Q =R
02· V(r) · r · dr .
Find Q for a blood vessel of radius R =1.6 mm.
65)
A)
512
375
p
Lv
B)
2048
1875
p
Lv
C)
512
625
p
Lv
D)
1024
625
p
Lv
66)
3
1
x3–x–1
x2dx
66)
A)
32
9
B)
64
9
C)
41
9
D)
125
36
67)
5
3
dx
x2– 4
67)
A)
–0.2506
B)
0.0626
C)
0.6044
D)
0.7175
68)
5
09 dx
68)
A)
14
B)
405
C)
90
D)
45
69)
1
06x5ex6 dx
69)
A)
e
B)
6e
C)
e – 1
D)
6e – 1
70)
y =6–x2; [–3, 1]
70)
A)
11
3
B)
–5
6
C)
–1
3
D)
49
6
71)
The rate of change of the population of a town is given by
P'(t) =1.9t
t –6,t > 10,
where P is the population in thousands t years after 1970. Find the function P(t) given that the
population in 1999 is 142 thousand.
71)
A)
P(t) =1.9t +1.9 ln (t –6) +81
B)
P(t) =142
(t –6)2+1.9 ln (t –6) +51
C)
P(t) =1.9t +11.4 ln (t –6) +51
D)
P(t) =11.4
t –6+ ln (t –6) +51
72)
(2x–1) ln(3x) dx
72)
A)
(x2 – x) ln (3x) – x2+ x + C
B)
(x2– x) ln (3x) –x2
2+ 2x + C
C)
x2
2– x ln (3x) –x2
4+ x + C
D)
(x2– x) ln (3x) –x2
2+ x + C
73)
(4x +3)2 dx
73)
A)
16x3+24x2+16x + C
B)
16
3x3+16x + C
C)
32x+24 + C
D)
16
3x3+12x2+9x + C
74)
8e4x dx
74)
A)
4e4x + C
B)
1
4 e4x + C
C)
1
2 e4x + C
D)
2e4x + C
75)
6
1t ln (t) dt
75)
A)
2.350167
B)
23.50167
C)
0.50167
D)
None of the above
Solve the problem.
76)
The velocity of particle A t seconds after its release is given by
va(t) =8.3t –0.5t2 (meters per second).
The velocity of particle B t seconds after its release is given by
vb(t) =11.4t –0.4t2 (meters per second).
How much farther does particle B travel than particle A during the first ten seconds (from t = 0 to t
= 10)? Round to the nearest meter.
76)
A)
188 m
B)
2 m
C)
255 m
D)
410 m
77)
77)
A)
Position in miles from starting point
B)
Final velocity in miles per hour
C)
Distance traveled in miles
D)
Acceleration in miles per hour per hour
78)
11x–6dx
78)
A)
55
x5+ C
B)
–11
5x–5+ C
C)
–66x–7+ C
D)
11
5x7+ C
79)
16
0( x – 3) dx
79)
A)
16
3; the shaded area above the x–axis minus the shaded area below the x–axis is equal to 16
3.
B)
–16
3; the shaded area above the x–axis minus the shaded area below the x–axis is equal to –
16
3.
C)
38
3; the total shaded area is equal to 38
3.
D)
16
3; the total shaded area is equal to 16
3.
80)
f(x) =17,g(x) =x2– 2x +2
80)
A)
x = –5 and x =5
B)
x = –3 and x =5
C)
x = 0 and x =5
D)
None exist.
23
Find the area of the shaded region.
81)
f(x) =x3+x2– 6x, g(x) = 6x
81)
A)
937
12
B)
343
12
C)
768
12
D)
81
12
82)
5
–16x5dx
82)
A)
93,744
B)
15,624
C)
–15,624
D)
624
83)
5x7 dx
83)
A)
40x8+ C
B)
40x7+ C
C)
35x6+ C
D)
5
8x8+ C
84)
x dx
16x2+48x +36
84)
A)
1
4ln(4x2+6x) + C
B)
1
16 ln(4x +6) +6
4x +6+ C
C)
1
36 ln(6x +4) +4
6x +4+ C
D)
x
4–3
8ln(4x +6) + C
85)
1
x2–25 dx
85)
A)
ln x +x2+25 + C
B)
1
10 ln 5+ x
5– x + C
C)
ln x +x2–25 + C
D)
1
10 ln x –5
x +5+ C
86)
y = x3, y = x2
86)
A)
5
12
B)
1
12
C)
1
6
D)
5
6
87)
Suppose that a velocity function is given by s‘(t) =7t4. Find the position function s(t) if s(0) =6.
87)
A)
s(t) =7
5t5+6
B)
s(t) =7
5t5
C)
s(t) =28t3+6
D)
s(t) =7t5+6
88)
y =ex;[0, 3]
88)
A)
e3– 1
B)
e3+ 1
9
C)
e3+ 1
3
D)
e3– 1
3
89)
Creamy Bugs Yogurt has found that the cost, in dollars per pound, of the yogurt it produces, is
C'(x) = –0.003x +5.50, for x 300,
where x is the number of pounds of yogurt produced. Find the total cost of producing 280 pounds
of yogurt.
89)
A)
$2844.80
B)
$5.08
C)
$1422.40
D)
$4.66
90)
e
1
19
xdx
90)
A)
–19
B)
19
C)
–19
2e2
D)
0
91)
5 x ln xdx
91)
A)
10
3x3/2 ln x–10
9x3/2 + C
B)
5x3/2 ln x–5x3/2 + C
C)
10
3x3/2 ln x–5
3x3/2 + C
D)
10
3x3/2 ln x+10
9x3/2 + C
92)
f'(x) =x5, f(0) =6
92)
A)
f(x) =x5+ 1
5+ 1 +6
B)
f(x) =x5
5+6
C)
f(x) =x5– 1
5– 1 +6
D)
f(x) =x5+ 1
5+6
93)
16
03 x dx
93)
A)
192
B)
128
C)
24
D)
288
94)
Find the area of the region bounded by y = 2x4–9x2, the x–axis, and the first coordinates of the
two relative minimum values of the function.
94)
A)
567
40
B)
972
5
C)
–972
5
D)
–567
40
95)
y = 7; [2, 9]
95)
A)
42
B)
14
C)
7
D)
49
96)
The rate of growth of a microbe population is given by m'(x) = 30xe2x, where x is time in days.
What is the growth after 1 day?
96)
A)
110.84
B)
62.52
C)
62.92
D)
55.42
97)
6x ln x dx
97)
A)
3x2 ln x –3
2x2+ C
B)
3x ln x –3
2x + C
C)
x2
2 ln x –x2
4+ C
D)
3x2 ln x –x2
4+ C
98)
y =1x; [1, 4]
98)
A)
4
B)
1
4
C)
2
D)
1
2
99)
y =1
2 x2, y = –x2+ 6
99)
A)
32
B)
4
C)
8
D)
16
100)
b
03exdx
100)
A)
3eb–3
B)
3eb– 1
C)
3eb + 1
b + 1 –e
2
D)
3eb
101)
16 +5x
x dx
101)
A)
216 +5x –4 ln 16 +5x –4
16 +5x +4+ C
B)
216 +5x + C
C)
16 +5x + ln 16 +5x –4
16 +5x +4+ C
D)
216 +5x +4 ln 16 +5x –4
16 +5x +4+ C
102)
f(x) = 0.02x3+ 11; interval [–8, 0]; 4 subintervals
102)
A)
56.00
B)
38.24
C)
76.48
D)
28.00
103)
y = x2, y = 4
103)
A)
37
3
B)
34
3
C)
31
3
D)
32
3
104)
The rate of growth of a microbe population is given by m'(x) = 30xe2x, where x is time in days.
What is the net growth between day 1 and day 3?
104)
A)
30,175
B)
15,073
C)
30,161
D)
15,062
105)
Rejoyne Inc. has a marginal–profit function given by
P'(x) = –3x +140, where P'(x) is in dollars per unit.
This means that the rate of change of total profit with respect to the number of units produced, x, is
P'(x). Find the total profit from the production and sale of the first 40 units.
105)
A)
$80
B)
$20
C)
$6400
D)
$3200
106)
(x4/3 – 3x5/2) dx
106)
A)
3
7 x7/3 –2
7 x7/2 + C
B)
3
4 x7/3 –4
7 x7/2 + C
C)
3
7 x7/3 –6
7 x7/2 + C
D)
3
4 x7/3 –3
7 x7/2 + C
107)
5
36 –x2 dx
107)
A)
5
6tan–1x
6+ C
B)
5
12 ln x –6
x +6+ C
C)
5sin–1x
6+ C
D)
5
12 ln x +6
x –6+ C
108)
13e6x
e6x + 1 dx
108)
A)
13 ln (e6x + 1) + C
B)
1
6 ln (e6x + 1) + C
C)
13
6 ln (e6x + 1) + C
D)
13
6(e6x + 1)–2+ C
109)
ln 7x dx
109)
A)
x ln 7x + x + C
B)
x ln 7x – x + C
C)
x ln 7x – 7x + C
D)
7x ln x – x + C
110)
2
–2(x3–4x) dx
110)
A)
16; the shaded area above the x–axis minus the shaded area below the x–axis equals 16.
B)
16; the shaded area above the x–axis plus the shaded area below the x–axis equals 16.
C)
4; the shaded area above the x–axis minus the shaded area below the x–axis equals 4.
D)
0; the shaded area above the x–axis is equal to the shaded area below the x–axis.
111)
5
0
1
4x dx
111)
A)
5
8
B)
200
C)
25
8
D)
25
4
112)
2
0(x +3)3 dx
112)
A)
48
B)
544
C)
136
D)
625
4
113)
Red Plains Roasting has found that the cost, in dollars per pound, of the peanuts it roasts, is
C'(x) = –0.015x +6.50, for x 500,
where x is the number of pounds of peanuts roasted. Find the total cost of roasting 250 pounds of
peanuts.
113)
A)
$1156.25
B)
$2.75
C)
$4.63
D)
$2312.50
114)
(5x +4) e–3x dx
114)
A)
–15x e–3x –57 e–3x + C
B)
–5
3 x e–3x –e–3x + C
C)
–5
3x e–3x –17
9e–3x + C
D)
5
3x e–3x +17
9e–3x + C
115)
f'(x) =5x2– 7x + 4, f(0) = 2
115)
A)
f(x) =5
3x3–7
2x2+ 4x – 4
B)
f(x) =5
3x3+7
2x2+ 4x + 2
C)
f(x) =5
3x3–7
2x2+ 4x + 2
D)
f(x) =5
3x3–7
2x2+ 4x – 2
116)
x
(7x2+ 3)5 dx
116)
A)
–7
3(7x2+ 3)–6+ C
B)
–7
3(7x2+ 3)–4+ C
C)
–1
14(7x2+ 3)–6+ C
D)
–1
56(7x2+ 3)–4+ C
117)
4x
2x +4dx
117)
A)
x(2x +4)1/2 –1
3(2x +4)3/2 + C
B)
4x(2x +4)1/2 +4
3(2x +4)3/2 + C
C)
4x(2x +4)1/2 –(2x +4)3/2 + C
D)
4x(2x +4)1/2 –4
3(2x +4)3/2 + C
118)
(x –7)2 dx
118)
A)
3x3–28x2+49x + C
B)
1
3x3–7x2+49x + C
C)
1
3x3+49x + C
D)
1
3x3+7x2–49x + C
119)
2
0(2 – x) dx
119)
A)
4
B)
2
C)
1
D)
8
120)
4
25x ln x dx
120)
A)
33.5
B)
6.70
C)
45.5
D)
7.9
121)
(x6+e2x) dx
121)
A)
x7
7+e2x + C
B)
x7
7+e2x
2+ C
C)
x7
7+e3x
3+ C
D)
x5
5+2e2x + C
122)
If f(x) 0 on the interval [a,b], then b
af(x) dx represents
i) the area to the right of the y–axis between y = a and y = b.
ii) the area above the x–axis between x = a and x = b.
iii) the area below the x–axis between x = a and x = b.
122)
A)
Both ii and iii could be correct.
B)
Only ii is correct.
C)
Only i is correct.
D)
None of the above
123)
3
0(4 –x2) dx
123)
A)
5; the total shaded area is equal to 5.
B)
3; the shaded area above the x–axis minus the shaded area below the x–axis is equal to 3.
C)
23
3; the total shaded area is equal to 23
3.
D)
23
3; the shaded area above the x–axis minus the shaded area below the x–axis is equal to 23
3.
124)
A computer manufacturer finds that the marginal supply for its new laptop computer satisfies the
function
S'(p) =110p
(27 – p)2,
where S is the quantity purchased when the price is p hundred dollars. Find the supply function
S(p) given that the company will sell 730 computers when the price is 18 hundred dollars.
124)
A)
S(p) =2970
(27 – p)2+ 110 ln (27 – p) + 180
B)
S(p) =2970
27 – p + 110 ln (27 – p) + 158
C)
S(p) =2970
(27 – p)2+ 110 ln (27 – p) + 158
D)
S(p) =2970
27 – p + 110 ln (27 – p) + 180
125)
(x3– 7x) dx
125)
A)
x4
4–7x2
2+ C
B)
x4
4+ 7x2+ C
C)
x3
3–7x2
2+ C
D)
3x2– 7 + C
126)
5 dx
x36 –x2
126)
A)
1
12 ln x –6
x +6+ C
B)
1
12 ln 6+ x
6– x + C
C)
ln x +x2–36 + C
D)
ln x +x2+36 + C
127)
14x1/3 dx
127)
A)
7
2x4+ C
B)
14x4/3 + C
C)
21
2x4/3 + C
D)
14
3x4/3 + C
128)
ln x
xn dx
128)
A)
1
1 – n x1 – n ln x –1
(1 – n)(2 – n)x2 – n + C
B)
1
1 – n x1 – n ln x +1
(1 – n)2x1 – n + C
C)
ln x –1
1 – nx1 – n + C
D)
1
1 – n x1 – n ln x –1
(1 – n)2x1 – n + C
129)
A car manufacturer finds that the marginal supply for its new station wagon satisfies the function
S'(p) =–7800
p(p –11) ,
where S is the quantity purchased in one town when the price is p thousand dollars. Find the
supply function S(p) given that the company will sell 622 cars when the price is 23 thousand
dollars.
129)
A)
S(p) =1
p –11 +7800
11 ln p
p –11 +161
B)
S(p) =7800
11 p + 85,800 ln (p –11) +161
C)
S(p) =7800
11 ln p
p –11 +161
D)
S(p) =7800
11 ln (p –11) +161
130)
130)
A)
Total volume
B)
Total mass in grams
C)
Area in square centimeters
D)
Mass per unit volume
131)
2x3x2+10dx
131)
A)
2
3x2(x2+10)3/2 +4
15(x2+10)5/2 + C
B)
2x2(x2+10)3/2 –2(x2+10)5/2 + C
C)
2
3x(x2+10)3/2 –4
5(x2+10)7/2 + C
D)
2
3x2(x2+10)3/2 –4
15(x2+10)5/2 + C
132)
f(x) =x3+x2+ 1; interval [0, 4]; 4 subintervals
132)
A)
135
B)
54
C)
134
D)
52
39
133)
(ln x)4
x dx
133)
A)
(ln x)5
5x + C
B)
(ln x)3
3+ C
C)
(ln x)5
5+ C
D)
(ln x)5+ C
134)
Accent Woodworkers knows that their marginal cost of producing x feet of custom molding is
given by
C'(x) = –0.00004x2–0.05x +90, for x 1000,
where C'(x) is in cents. Approximate their total cost, in dollars, of manufacturing 1000 feet of
molding, using 5 subintervals over [0, 1000] and the left endpoint of each subinterval.
134)
A)
$302.00
B)
$1004.00
C)
$699.84
D)
$604.00
135)
1
–1(x2–x4) dx
135)
A)
–1
15; the area bounded by the x–axis and the graph of y =x2–x4 is –1
15.
B)
–2
15; the area bounded by the x–axis and the graph of y =x2–x4 is –2
15.
C)
4
15; the area bounded by the x–axis and the graph of y =x2–x4 is 4
15.
D)
2
15; the area bounded by the x–axis and the graph of y =x2–x4 is 2
15.
136)
1
03x 51 +x2 dx
136)
A)
5
252
B)
5
2(26/5 – 1)
C)
3
2(26/5 – 1)
D)
5
4(26/5 – 1)
137)
7
–33 dx
137)
A)
12
B)
10
C)
15
D)
30
138)
y =xn; [5, 8]
138)
A)
8n+1–5n+1
3
B)
8n+1–5n+1
(n+1)
C)
13
2n
D)
8n+1–5n+1
3(n+1)
139)
x3–9x +6
x2 dx
139)
A)
x2
2–9
2x2–6
x+ C
B)
x2–9 ln x+6
x+ C
C)
x2
2+9
x2–12
x3+ C
D)
x2
2–9 ln x–6
x+ C
140)
f(x) =x3+ 2x2– 3x, g(x) = 0
140)
A)
95
12
B)
81
12
C)
–81
12
D)
47
12
Answer:
A
Explanation:
A)
B)
C)
D)
Evaluate.
141)
3
2
dt
1 + t
141)
A)
ln 4
3
B)
–3
4
C)
ln 3
2
D)
1
2
Answer:
A
Explanation:
A)
B)
C)
D)
142)
Areas of complicated regions are estimated by filling in with shapes whose area is easy to compute.
The shape that is most often used in defining the definite integral is ? .
142)
A)
the triangle
B)
the square
C)
the rectangle
D)
the circle
Answer:
C
Explanation:
A)
B)
C)
D)
143)
6
–1 x dx
143)
A)
7
B)
37
2
C)
35
2
D)
37
144)
4
0(15 – 2x) dx
144)
A)
44
B)
76
C)
52
D)
31
145)
116
x dx
145)
A)
ln x
116 + C
B)
116x + C
C)
58x–2+ C
D)
116 ln x + C
146)
A kitchen remodeling company determines that the marginal cost, in dollars per foot, of installing
x feet of kitchen countertop is given by
C'(x) = 7x–1/3.
Find the cost of installing an extra 13 feet of countertop after 30 feet have already been ordered.
146)
A)
$58.05
B)
$27.50
C)
$257.75
D)
$55.00
147)
y =5x +1; [2, 5]
147)
A)
37
2
B)
111
2
C)
5
D)
36
148)
A particle is released during an experiment. Its speed t minutes after release is given by
v(t) = –0.25t2+ 8t,
where v(t) is in kilometers per minute. How far does the particle travel during the first 14 minutes?
148)
A)
63.00 km
B)
555.33 km
C)
784 km
D)
882.00 km
149)
28x
x dx
149)
A)
14
3 x1/2 + C
B)
56
3 x3/2 + C
C)
28
3 x3/2 + C
D)
28
3 x1/2 + C
150)
2
-1
(x3– 4x) dx
150)
A)
–9
4; the area between the x–axis and the graph of y =x3– 4x over the interval [–1, 0] minus
the area between the x–axis and the graph of y =x3– 4x over the interval [0, 2] is –9
4.
B)
9; the area under the graph of y =x3– 4x over the interval [–1, 2] is 9.
C)
3; the area between the x–axis and the graph of y =x3– 4x over the interval [–1, 0] minus the
area between the x–axis and the graph of y =x3– 4x over the interval [0, 2] is 3.
D)
–9
4; the area between the x–axis and the graph of y =x3– 4x over the interval [–1, 2] is –9
4.
151)
(x –5)(4x +2) dx
151)
A)
8x –18 + C
B)
4
3x3–9x2–10x + C
C)
4
3x3–10x2–10x + C
D)
4x3–18x2–10x + C
152)
f(x) = –9, g(x) =x2– 2x + 1
152)
A)
x = –2 and x =4
B)
x = 0 and x =4
C)
x = –4 and x =4
D)
None exist.
153)
8e3x dx
153)
A)
24e3x + C
B)
8
3x+1e3x+1+ C
C)
8
3 ln 3x + C
D)
8
3e3x + C
154)
b
0cecx dx
154)
A)
c2(ebc – 1)
B)
ebc – 1
c
C)
ebc – 1
D)
c(ebc – 1)
155)
x = 0, x = –2, y = ex, y = 0
155)
A)
0.68
B)
0.78
C)
0.86
D)
0.96
156)
e2x
5ex+6 dx
156)
A)
ex
5–6
25 ln (5ex+6) + C
B)
6
5ex+6+ ln (5ex+6 ) + C
C)
x
5–6
25 ln (5x +6) + C
D)
ex
5+6
25 sin–15ex+6+ C
157)
19
2 + 5y dy
157)
A)
19
5 ln 2 + 5y + C
B)
18
5 ln 2 + 5y + C
C)
18 ln 2 + 5y + C
D)
19 ln 2 + 5y + C
158)
f(x) =x2+ 2x –3, g(x) = 2x +1
158)
A)
x = –4 and x =4
B)
x = –2 and x =2
C)
x = –1.4142136 and x =1.41421356
D)
None exist.
159)
5
05x dx
159)
A)
50
3
B)
5
C)
75
2
D)
25
160)
1
0(3x +4)(3x –5) dx
160)
A)
– 17
B)
–37
2
C)
–14
D)
18
161)
y = x2– 5x + 4, y = –(x – 1)2
161)
A)
8
9
B)
8
7
C)
9
8
D)
7
8
162)
f(x) = –0.02x4– 0.2x2+ 10; interval [–4, 4]; 4 subintervals
162)
A)
58.88
B)
30.28
C)
29.44
D)
60.56
49
163)
163)
A)
Total area in square feet
B)
Rate of change of price
C)
Rate of change of area
D)
Total cost in dollars
D
164)
Hatts and Company determines that its marginal cost, in dollars per hat, is given by
C'(x) = – 1
40x +40, for x 350.
Find the total cost of producing the first 260 hats.
164)
A)
$19,110.00
B)
$9555.00
C)
$33.50
D)
$36.75
B
165)
The first derivative of a person’s body temperature, with respect to the dosage of x milligrams of a
drug, is given by D'(x) =8
x + 2. One milligram raises the temperature 3.2° C. Find the function D(x)
giving the total change in temperature as a function of x.
165)
A)
D(x) =8 ln x + 2 + 3.2
B)
D(x) = ln 8
x + 2 + 5.6
C)
D(x) = ln 8
x + 2 – 3.2
D)
D(x) =8 ln x + 2 – 5.6
D
166)
x8(x9– 4)4 dx
166)
A)
(x9–4)3
27 + C
B)
(x9–4)5+ C
C)
(x9–4)5
9+ C
D)
(x9–4)5
45 + C
167)
11x2e–4x3 dx
167)
A)
12 e–4x3+ C
B)
11
12 e–4x3+ C
C)
–11 e–4x3+ C
D)
–11
12 e–4x3+ C
168)
y =x2+ 1; [0, 1]
168)
A)
1
3
B)
5
3
C)
4
3
D)
2
3
169)
The area under the graph of f over the interval [–3, 5]
f(x) =4, if x < 1,
4x2,if x 1
169)
A)
32
B)
512
C)
875
3
D)
544
3
170)
Find a company’s total–cost function if its marginal cost function is C'(x) =5x2– 7x + 4 and C(6) =
260.
170)
A)
C(x) =5
3x3–7
2x2+ 4x – 260
B)
C(x) =5
3x3–7
2x2+ 4x – 2
C)
C(x) =5
3x3–7
2x2+ 4x + 260
D)
C(x) =5
3x3–7
2x2+ 4x + 2
171)
A company finds that consumer demand quantity changes with respect to price at a rate given by
D'(p) = – 2000
p2. Find the demand function if the company knows that 834 units of the product are
demanded when the price is $5 per unit.
171)
A)
D(p) =2000
p3+434
B)
D(p) =2000
p+834
C)
D(p) =2000
p+434
D)
D(p) =4000
p+834
172)
A well–drilling company finds that its marginal profit, in dollars, from drilling a well that is x feet
deep is given by
P'(x) =3x.
Find the company’s profit from drilling a well that is 220 feet deep.
172)
A)
$1770.80
B)
$1328.10
C)
$2175.42
D)
$996.07
173)
1
x ln x6 dx
173)
A)
1
6ln x6+ C
B)
ln(ln x6) + C
C)
ln x6+ C
D)
1
6ln(ln x6) + C
Write summation notation for the expression.
174)
h(x1) +h(x2) +h(x3) +h(x4) +h(x5) +h(x6)
174)
A)
x6
i=x1h(i)
B)
6
i=1h(i)
C)
6
i=1h(xi)
D)
x6
i=x1i
175)
2
1(x –3) e2xdx
175)
A)
–31.71
B)
–268.48
C)
–50.18
D)
–87.03
176)
1
x (ln x)13 dx
176)
A)
–1
12(ln x)12 + C
B)
–1
12x (ln x)12 + C
C)
1
x (ln x)14 + C
D)
–1
14(ln x)14 + C
177)
7
–7(2x +14) dx
177)
A)
392
B)
196
C)
98
D)
28
178)
3
–1(x4+ 2x3– 2x2– x – 1) dx
178)
A)
10.0667
B)
13.0667
C)
–10.9333
D)
62.1333
179)
1
0
6 x dx
16 +3x2
179)
A)
19 –4
B)
219 –8
C)
19
2–2
D)
–219 +8
180)
y =x2(x – 2)2; [0, 2]
180)
A)
17
15
B)
16
15
C)
15
17
D)
15
16
181)
x7
ex8 dx
181)
A)
7x6
ex8+ C
B)
–1
8ex8+ C
C)
1
ex8+ C
D)
–1
8ex8–1+ C
182)
y = 2x – x2, y = 2x – 4
182)
A)
37
3
B)
34
3
C)
32
3
D)
31
3
183)
8
(y – 9)3 dy
183)
A)
–2
(y – 9)4+ C
B)
–4
(y – 9)2+ C
C)
4
(y – 9)2+ C
D)
2
(y – 9)4+ C
184)
8
06x dx
184)
A)
67
B)
384
C)
192
D)
24
185)
i=19i
185)
A)
9+18 +27 +36 +45
B)
9+45
C)
1 + 2 + 3 + 4 + 5
D)
4 + 4 + 4 + 4 + 4
Solve the problem.
186)
An object moves in such a way that its velocity (in meters per second) after time t (in seconds) is
given by
v = t2+ 4t + 3.
Find the distance traveled by the object during the first four seconds.
186)
A)
35.0 m
B)
65.3 m
C)
44.0 m
D)
53.3 m
187)
A car accelerates at a constant rate from 0 mph to 59 mph in 30 seconds. How far does the car travel
during this time?
187)
A)
0.4917 mi
B)
0.2458 mi
C)
0.1639 mi
D)
0.9833 mi
188)
5
4(t +7 ) (t –7 ) dt
188)
A)
54
B)
40
3
C)
–128
3
D)
–2
Solve the problem.
189)
Suppose that in a memory experiment the rate of memorizing is given by
M'(t) = –0.006t2+ 0.4t,
where M'(t) is the memory rate, in words per minute. How many words are memorized in the first
20 minutes (from t = 0 to t =20)?
189)
A)
24 words
B)
144 words
C)
104 words
D)
64 words
190)
In town A, the birth rate is given by
b'(t) =51e0.27t (births per year),
where t is the number of years since 2000. In town B, the birth rate is given by
B'(t) =85e0.42t (births per year),
where t is the number of years since 2000. How many more births are there in town B than in town
A from 2000 to 2010 (from t = 0 to t = 10)?
190)
A)
13,294 births
B)
4875 births
C)
10,672 births
D)
10,685 births
191)
6x248+4x3 dx
191)
A)
6(8 +4x3)5/4 + C
B)
–4(8 +4x3)–3/4 + C
C)
2
5(8 +4x3)5/4 + C
D)
24
5(8 +4x3)5/4 + C
192)
3
1ln 4x dx
192)
A)
–1.93
B)
8.07
C)
11.1
D)
4.07
193)
f(x1) +f(x2) + . . . +f(x20)
193)
A)
x20
i=x1i
B)
20
i=1f(xi)
C)
x20
i=x1f(i)
D)
20
i=1f(i)
194)
(4x2– 6x) dx
194)
A)
4
3x3–3x2+ C
B)
4
3x3+ C
C)
4
3x2+3x + C
D)
–4
3x3–3x2+ C
195)
5
–28x3 dx
195)
A)
– 1218
B)
– 2436
C)
1282
D)
2564
196)
3(ln x)2 dx
196)
A)
3x (ln x)2–6x ln x –6x + C
B)
3x (ln x)2–6x ln x + C
C)
x (ln x)2– 2x ln x + 2x + C
D)
3x (ln x)2–6x ln x +6x + C
197)
y =x2–3x +5; [0, 3]
197)
A)
11
4
B)
27
2
C)
7
2
D)
5
Solve the problem.
198)
A company has found that its expenditure rate per day (in hundreds of dollars) on a certain type of
job is given by E'(x) =12x + 12, where x is the number of days since the start of the job. Find the
expenditure if the job takes 7 days.
198)
A)
$9600
B)
$96
C)
$378
D)
$37,800
199)
(9t2+ 7t – 2)dt
199)
A)
18t + 7 + C
B)
9t3+ 7t2– 2t + C
C)
9
2t3+ 7t2– 2t + C
D)
3t3+7
2t2– 2t + C
200)
12x3x dx
200)
A)
8
3x9/2 + C
B)
2
9x9/2 + C
C)
11
5x9/2 + C
D)
24
7x9/2 + C
Answer Key
Testname: C4
Answer Key
Testname: C4
61
Answer Key
Testname: C4
Answer Key
Testname: C4