Find the integral.
127)
x4x5+1 dx
127)
A)
2
3(x5+1)3/2 + C
B)
2
15 (x5+1)3/2 + C
C)
1
10 x5+1
+ C
D)
2
15 x5(x5+1)3/2 + C
Use n = 4 to approximate the value of the integral by Simpson’s rule.
128)
3
1
(4x +6) dx
128)
A)
28
B)
14
C)
70
3
D)
56
Find the integral.
129)
te–7t2 dt
129)
A)
1
7e–7t2+ C
B)
–1
7e–7t2+ C
C)
–1
14 e–7t2+ C
D)
1
14 e–7t2+ C
Find the exact value of the integral using a formula from geometry.
130)
5
0
25 –x2 dx
130)
A)
25
4
B)
50
C)
25
D)
25
2
Find the area of the shaded region.
131)
y = 7
131)
A)
14
B)
49
C)
42
D)
7
Use n = 4 to approximate the value of the integral by Simpson’s rule.
132)
2
0
9x2 dx
132)
A)
21
B)
99
4
C)
24
D)
12
Find the integral.
133)
dr
6r – 7
133)
A)
1
66r – 7 + C
B)
1
46r – 7 + C
C)
1
36r – 7 + C
D)
1
26r – 7 + C
134)
(ln x)3
x dx
134)
A)
(ln x)4
4x + C
B)
(ln x)4
4+ C
C)
(ln x)2
2+ C
D)
(ln x)4+ C
Find the area between the curves.
135)
x = 1, x =4, y = ln x , y = ln 3x
135)
A)
ln 27 –6
B)
ln 3
C)
ln 81
D)
ln 27
Solve the problem.
136)
The velocity of particle A, t seconds after its release is given by va(t) =2.8e0.5t meters per second.
The velocity of particle B, t seconds after its release is given by
vb(t) =12.8t –0.4t2 meters per second. If velocity is measured in meters per second, how much
farther does particle A travel than particle B during the first ten seconds (from t = 0 to t = 10)?
Round to the nearest meter.
136)
A)
186 m
B)
586 m
C)
324 m
D)
319 m
Find the integral.
137)
15x–8 dx
137)
A)
–15
7x9+ C
B)
–120
x9+ C
C)
–105
x7+ C
D)
–15
7x7+ C
Solve the problem.
138)
The rate of expenditure for maintenance of a particular machine is given by M'(x) =9x x2+ 5,
where x is time measured in years. Total maintenance costs through the second year are $51. Find
the total maintenance function.
138)
A)
M(x) =3(x2+ 5)3/2 – 30
B)
M(x) =3(x2+ 5)3/2 + 42
C)
M(x) =9(x2+ 5)3/2 – 30
D)
M(x) =9(x2+ 5)3/2 + 42
Find the integral.
139)
23x dx
139)
A)
23x
3 ln 2+ C
B)
23x
3+ C
C)
24x
4+ C
D)
23x
ln 2+ C
Solve the problem.
140)
The number of books in a small library increases at a rate according to the function
B(t) =270e0.05t, where t is measured in years after the library opens. How many books will the
library have 1 year(s) after opening?
140)
A)
14
B)
5400
C)
284
D)
277
Find the integral.
141)
7x242+3x3 dx
141)
A)
28
45 (2 +3x3)5/4 + C
B)
–14
3(2 +3x3)–3/4 + C
C)
7(2 +3x3)5/4 + C
D)
28
5(2 +3x3)5/4 + C
Evaluate the definite integral.
142)
4
1
(x3/2 + x1/2 – x–1/2) dx
142)
A)
44
3
B)
224
15
C)
46
D)
226
15
Find the area of the shaded region.
143)
y =x3– 4x
143)
A)
9
4
B)
41
4
C)
33
4
D)
17
4
Evaluate the definite integral.
144)
9
4
t2+ 1
t dt
144)
A)
212
B)
447
5
C)
432
5
D)
472
5
Find the integral.
145)
(7x–4– 8x–1 ) dx
145)
A)
7
4 x–3+ 8 ln x+ C
B)
–7
3x–3+ 8 ln x+ C
C)
7
4x–3– 8 ln x+ C
D)
–7
3x–3– 8 ln x+ C
Evaluate the definite integral.
146)
0
–1
(2 + x2)dx
146)
A)
0
B)
2
C)
–2
D)
7
3
Solve the problem.
147)
Joe wants to find out how far it is across the lake. His boat has a speedometer but no odometer. The
table below shows the boat’s velocity at 10–second intervals. Estimate the distance across the lake
using right endpoints.
Time
(sec)
Velocity
(ft/sec)
0
10
20
30
40
50
60
70
80
90
100
0
12
30
55
52
57
54
57
47
15
0
147)
A)
3790 ft
B)
379 ft
C)
3890 ft
D)
5700 ft
42
Find the integral.
148)
(y – 1)7 dy
148)
A)
1
2 y2+1
8(y – 1)8+ C
B)
1
9(y – 1)9+1
8(y – 1)8+ C
C)
1
16(y – 1)8+ C
D)
1
8(y – 1)8+ C
Solve the problem.
149)
A company determines that its marginal revenue per day is given by R’(t) =110et, and that R(0) = 0,
where R(t) = revenue, in dollars, on the tth day. The company’s marginal cost per day is given by
C'(t) =120 –0.2t, and that C(0) = 0, where C(t) = cost, in dollars, on the tth day. Find the total profit
from t = 0 to t =7 (the first 7 days). Round your answer to the nearest dollar.
Note: P(T) = R(T) – C(T) =
T
0
[R'(t) – C'(t)] dt.
149)
A)
$119,689
B)
$119,795
C)
$119,685
D)
$119,675
Use the definite integral to find the area between the x–axis and f(x) over the indicated interval.
150)
f(x) =x4– 4x3+ 4x2; [0, 2]
150)
A)
16
15
B)
17
15
C)
15
16
D)
15
17
Evaluate the definite integral.
151)
1
0
10r
9+5r2 dr
151)
A)
– 2 14 +6
B)
214 –6
C)
14 –3
D)
14
2–3
2
Use your calculator to approximate the integral using the method indicated, with n = 100. Round your answer to four
decimal places.
152)
2
0
4+1
x + 3 dx (Simpson’s rule)
152)
A)
8.5108
B)
8.4574
C)
8.5264
D)
8.4435
Use n = 4 to approximate the value of the integral by Simpson’s rule.
153)
4
0
x dx
153)
A)
16
B)
8
C)
4
D)
20
3
Solve the problem.
154)
A swimming pool has a leak, and the leak is getting worse. The table below gives the leakage rate
every 6 hours. Use right endpoints to estimate the number of gallons lost in 48 hours.
Time
(hr)
Leakage
(gal/hr)
0
6
12
18
24
30
36
42
48
0
0.6
1.3
1.9
3.0
4.5
5.9
7.0
8.3
154)
A)
145.2 gal
B)
32.5 gal
C)
195 gal
D)
255 gal
155)
A company has found that its rate of expenditure (in hundreds of dollars) on a certain type of job is
given by
E'(x) =6x + 4,
where x is the number of days since the start of the job. Find the total expenditure if the job takes 2
days.
155)
A)
$16
B)
$1600
C)
$2000
D)
$20
Find the integral.
156)
x
6+6
x dx
156)
A)
1
6x +C
B)
x +C
C)
x ln 6 + 6 ln x+ C
D)
1
12 x2+ 6 ln x+ C
Answer the question, concerning the use of substitution in integration.
157)
If we decide to use u = ex2, then which of the following are correct?
i) du = 2e dx
ii) x2=u
e
iii) du = 2ex dx
iv) du =2x
e dx
157)
A)
Both i and iii
B)
Both ii and iii
C)
Only iii
D)
None of the above
Find the integral.
158)
t2+2
t3+6t + 2 dt
158)
A)
3 ln t3+6t + 2 + C
B)
–3
(t3+6t + 2)2+ C
C)
–1
3(t3+6t + 2)2+ C
D)
ln t3+6t + 2
3+ C
159)
19
2 + 5y dy
159)
A)
18
5 ln 2 + 5y + C
B)
18 ln 2 + 5y + C
C)
19 ln 2 + 5y + C
D)
19
5 ln 2 + 5y + C
Provide the proper response.
160)
If f(x) 0 on the interval [a, b], then
b
a
f(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.
160)
A)
Only ii is correct.
B)
Only iii is correct.
C)
Either ii or iii could be correct.
D)
Only i is correct.
D)
Find the integral.
161)
ln x5
x dx
161)
A)
1
ln x5+ C
B)
1
2(ln x5)2+ C
C)
1
5(ln x5)2+ C
D)
1
10 (ln x5)2+ C
Use the definite integral to find the area between the x–axis and f(x) over the indicated interval.
162)
f(x) = 2x – x2; [0, 2]
162)
A)
7
3
B)
5
3
C)
2
3
D)
4
3
Find the area between the curves.
163)
y = x2, y = 4
163)
A)
37
3
B)
32
3
C)
34
3
D)
31
3
Evaluate the definite integral.
164)
4
1
t8–t4
t6dt
164)
A)
259
12
B)
81
4
C)
79
4
D)
275
12
Answer Key
Testname: C7
Answer Key
Testname: C7
Answer Key
Testname: C7
Answer Key
Testname: C7