87)
An auxiliary fuel tank for a helicopter is shaped like the surface generated by revolving the curve
y = 1 –x2
16 , –4 x 4, about the x–axis (dimensions are in feet). How many cubic feet of fuel will
the tank hold to the nearest cubic foot?
87)
A)
7 cubic ft
B)
17 cubic ft
C)
4 cubic ft
D)
13 cubic ft
The function represents the rate of flow of money in dollars per year. Assume a 10–year period and find the present
value.
88)
f(x) =0.09x +700 at 7% compounded continuously
88)
A)
$14,999.73
B)
$3874.62
C)
$5037.01
D)
$4197.51
Use integration by parts to find the integral.
89)
5x ln x dx
89)
A)
5
2x2 ln x –x2
4+ C
B)
5
2x ln x –5
4x + C
C)
5
2x2 ln x –5
4x2+ C
D)
x2
2 ln x –x2
4+ C
Solve the problem. Round your answer to the nearest whole number.
90)
The capital value of an asset is defined as
0
R(t)e–rt dt , where k is the annual rate of interest
compounded continuously and R(t) gives the annual rate at which earnings are produced by the
asset at time t. Find the capital value of an asset that produces $5000 yearly income at 9%
compounded continuously.
90)
A)
$55,000
B)
$62,500
C)
$55,556
D)
$50,000
Find the average value of the function on the given interval.
91)
f(x) = x3– 3x2+ 3x – 1; [0, 2]
91)
A)
1
B)
1
2
C)
1
4
D)
0
Find the volume of the solid of revolution formed by rotating about the x–axis the region bounded by the curves.
92)
y =ex, y = 0, x = – 2, x =6 Give your answer in exact form.
92)
A)
(e12 –e–4)
B)
2(e6–e–2)
C)
2(e12 –e–4)
D)
2(e6–e–2)
Use integration by parts to find the integral.
93)
x2ln 4x dx
93)
A)
1
3 x3 ln 4x –1
9 x3+ C
B)
ln 4x –1
3 x3+ C
C)
1
3x3 ln 4x –1
12 x4+ C
D)
1
3x3 ln 4x +1
9 x3+ C
Find the integral by using integration by parts or other techniques. Round the answer to four decimal places if necessary.
94)
(2x – 1) ln(2x) dx
94)
A)
(x2– x) ln 2x –x2
2+ 2x + C
B)
(x2 – x) ln 2x – x2+ x + C
C)
(x2
2– x) ln 2x –x2
4+ x + C
D)
(x2– x) ln 2x –x2
2+ x + C
Find the average value of the function on the given interval.
95)
f(x) =x2e5x; [0, 5] Give your answer in exact form.
95)
A)
577
125e25 –2
125
B)
577
625e25
C)
17
5e25 –2
5
D)
577
625e25 –2
625
The function represents the rate of flow of money in dollars per year. Assume a 10–year period and find the present
value.
96)
f(x) = 500 at 5% compounded continuously
96)
A)
$3934.69
B)
$16,065.31
C)
$6065.31
D)
$6487.21
Use integration by parts to find the integral. Round the answer to two decimal places if necessary.
97)
7
0
xexdx
Give your answer in exact form.
97)
A)
8e7+ 1
B)
6e7
C)
6e7+ 1
D)
6e7– 1
Use the table of integrals or a computer or calculator with symbolic integration capabilities to find the integral.
98)
1
x2–4
dx
98)
A)
1
4 ln 2+ x
2– x + C
B)
1
4 ln x –2
x +2+ C
C)
ln x +x2–4+ C
D)
ln x +x2+4+ C
Evaluate the improper integral. If the integral does not converge, state that the integral is divergent.
99)
0
–
7xe3x dx
99)
A)
1.7778
B)
–0.7778
C)
0
D)
Divergent
The function represents the rate of flow of money in dollars per year. Assume a 10–year period and find the present
value.
100)
f(x) = 500e0.04x at 8% compounded continuously
100)
A)
$6147.81
B)
$4121.00
C)
$20,879.00
D)
$18,647.81
Solve the problem. Round your answer to the nearest whole number.
101)
The capital value of an asset is defined as
0
R(t)e–rt dt , where k is the annual rate of interest
compounded continuously and R(t) gives the annual rate at which earnings are produced by the
asset at time t. Suppose income from an investment starts (at time 0) at $8000 a year and increases
linearly and continuously at a rate of $300 per year. Find the capital value at an interest rate of 6%
compounded continuously.
101)
A)
$138,333
B)
$133,333
C)
$216,667
D)
$2,222,222
Provide the proper response.
102)
A student knows that
a
f(x) dx =81. Can
–1
–
f(x) dx be found, and if so, what is it?
102)
A)
Yes, –81
B)
No
Solve the problem. Round your answer to the nearest whole number.
103)
The capital value of an asset is defined as
0
R(t)e–rt dt , where k is the annual rate of interest
compounded continuously and R(t) gives the annual rate at which earnings are produced by the
asset at time t. Find the capital value of an asset that produces $5000 yearly income at 8%
compounded continuously.
103)
A)
$60,500
B)
$71,429
C)
$65,000
D)
$62,500
Find the average value of the function on the given interval.
104)
f(x) = ex/2; [0, 14]
104)
A)
39.10
B)
78.20
C)
156.52
D)
156.55
Evaluate the improper integral. If the integral does not converge, state that the integral is divergent.
105)
0
–
5 e6x dx
105)
A)
–5
B)
0
C)
5
6
D)
Divergent
Solve the problem.
106)
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?
106)
A)
55.42
B)
62.52
C)
110.84
D)
62.92
107)
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.
107)
A)
2.05
B)
1.92
C)
0.38
D)
7.86
108)
The rate of a continuous money flow starts at $500 and increases exponentially at 4% per year for
10 years. Find the present value if interest is earned at 8% compounded continuously.
108)
A)
$4121.00
B)
$20,879.00
C)
$18,647.81
D)
$6147.81
D)
Find the integral by using integration by parts or other techniques. Round the answer to four decimal places if necessary.
109)
15x2 e2x dx
109)
A)
15
4e2x(x2– x + 1) + C
B)
15e2x(2x2– 2x + 1) + C
C)
15
2e2x(2x2– 2x + 1) + C
D)
15
4e2x(2x2– 2x + 1) + C
D)
Solve the problem.
110)
The rate of water usage for a business, in gallons per day, is given by W(t) =632te–t, where t
represents the number of hours since midnight. Approximately how many gallons of water does
the business use in the first 6 hours of the day?
110)
A)
643 gallons
B)
624 gallons
C)
11 gallons
D)
621 gallons
D)
111)
A real estate investment is expected to produce a uniform continuous rate of money flow of $2000
per year for 10 years. Find the final amount at an interest rate of 2% compounded continuously.
111)
A)
$100,000.00
B)
$22,140.28
C)
$27,042.19
D)
$222,140.28
D)
D)
The function represents the rate of flow of money in dollars per year. Assume a 10–year period and find the present
value.
112)
f(x) = 1000e–0.04x at 7% compounded continuously
112)
A)
$18,219.69
B)
$27,310.60
C)
$6064.81
D)
$12,117.01
The function represents the rate of flow of money in dollars per year. Assume a 10–year period and find the accumulated
amount of money flow at t = 10.
113)
f(x) = 0.5x at 7% compounded continuously
113)
A)
$378.95
B)
$174.87
C)
$32.02
D)
$64.04
Evaluate the improper integral. If the integral does not converge, state that the integral is divergent.
114)
–4
–
6
x3 dx
114)
A)
0
B)
3
8
C)
3
16384
D)
–3
16
Determine whether the improper integral is convergent or divergent.
115)
2
25
x2 dx
115)
A)
Divergent
B)
Convergent
Solve the problem.
116)
Suppose the number of items a new worker on an assembly line produces daily after t days on the
job is given by 25 + 2t. Find the average number of items produced daily in the first 10 days.
116)
A)
38
B)
350
C)
40
D)
35
Use integration by parts to find the integral.
117)
e2x x2 dx
117)
A)
1
2x2e2x –1
2xe2x +1
4e2x + C
B)
1
2x2e2x –1
2xe2x + C
C)
1
2x2e2x –1
4xe2x +1
4e2x + C
D)
1
2x2e2x – xe2x +1
4e2x + C
Evaluate the improper integral. If the integral does not converge, state that the integral is divergent.
118)
0
12
(x + 1)2 dx
118)
A)
12
B)
0
C)
–12
D)
Divergent
Determine whether the improper integral is convergent or divergent.
119)
–
3xe–x2 dx
119)
A)
Divergent
B)
Convergent
120)
1
2x +5
x2+5x + 1
120)
A)
Convergent
B)
Divergent
Find the area between the graph of the function and the x–axis over the given interval, if possible.
121)
f(x) =1
x +3 for (–1, )
121)
A)
1
9
B)
ln 3
C)
1
D)
Divergent
Solve the problem. Round your answer to the nearest whole number.
122)
The capital value of an asset is defined as
0
R(t)e–rt dt , where k is the annual rate of interest
compounded continuously and R(t) gives the annual rate at which earnings are produced by the
asset at time t. Find the capital value of an asset that produces $5000 yearly income at 6%
compounded continuously.
122)
A)
$85,000
B)
$100,000
C)
$83,333
D)
$80,000
The function represents the rate of flow of money in dollars per year. Assume a 10–year period and find the accumulated
amount of money flow at t = 10.
123)
f(x) = 500 at 4% compounded continuously
123)
A)
$9171.45
B)
$6147.81
C)
$31,147.81
D)
$12,500.00
Solve the problem.
124)
Find the area between y = ln x and the x–axis from x = 1 to x =5. Give your answer in exact form.
124)
A)
4
5
B)
5 ln 5– 4
C)
5 ln 5–5
D)
ln 5
The function represents the rate of flow of money in dollars per year. Assume a 10–year period and find the accumulated
amount of money flow at t = 10.
125)
f(x) = 0.05x +700 at 2% compounded continuously
125)
A)
$7751.77
B)
$7047.07
C)
$6459.81
D)
$78,051.77
D)
Evaluate the improper integral. If the integral does not converge, state that the integral is divergent.
126)
2
e–5x dx Give your answer in exact form.
126)
A)
0
B)
e–10
5
C)
–e–10
D)
Divergent
D)
Solve the problem.
127)
The rate of a continuous money flow starts at $1000 and decreases exponentially at 4% per year for
10 years. Find the present value if interest is earned at 2% compounded continuously.
127)
A)
$7519.81
B)
$13,701.98
C)
$25,813.53
D)
$30,368.65
D)
Use integration by parts to find the integral. Round the answer to two decimal places if necessary.
128)
3
1
ln 5x dx
128)
A)
8.51
B)
14.4
C)
4.51
D)
–3.49
D)
Solve the problem.
129)
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?
129)
A)
15,073
B)
30,175
C)
30,161
D)
15,062
Determine whether the improper integral is convergent or divergent.
130)
–
6x2+2
2x3+2x +7 dx
130)
A)
Divergent
B)
Convergent
Find the volume of the solid of revolution formed by rotating about the x–axis the region bounded by the curves.
131)
f(x) =x, y = 0, x = 1, x =16
131)
A)
7.5
B)
255
C)
128
D)
127.5
Use integration by parts to find the integral. Round the answer to two decimal places if necessary.
132)
2
0
(x – 4) ln x dx
132)
A)
0.39
B)
2.84
C)
–1.31
D)
–7.61
Determine whether the improper integral is convergent or divergent.
133)
1
9
x dx
133)
A)
Divergent
B)
Convergent