Solve the problem. Round your answer to the nearest whole number.
134)
The rate of a reaction to a drug is given by r'(t) =6t2e–t, where t is the number of hours since the
drug was administered. Find the total reaction to the drug over all the time since it was
administered, assuming this is an infinite time interval. (Hint: lim
t tke–t= 0 for all real numbers k.)
134)
A)
12
B)
C)
0
D)
36
Use the table of integrals or a computer or calculator with symbolic integration capabilities to find the integral.
135)
9
x2+16
dx
135)
A)
9 ln x +x2+16 + C
B)
9
4tan–1x
4+ C
C)
9 ln x +x2+4+ C
D)
–9
4 ln 4+x2+16
x+ C
Use integration by parts to find the integral. Round the answer to two decimal places if necessary.
136)
5
2
x 5 – x dx
136)
A)
2.77
B)
9.01
C)
–11.09
D)
11.09
137)
2
1
(x –9)e4xdx
137)
A)
–5515.60
B)
–128,541.44
C)
–23,356.28
D)
–5290.38
Solve the problem.
138)
An auxiliary fuel tank for a helicopter is shaped like the surface generated by revolving the curve
y = 1 –x2
25 , –5 x 5, about the x–axis (dimensions are in feet). If a cubic foot holds 7.481 gallons
and the helicopter gets 3 miles to the gallon, how many additional miles will the helicopter be able
to fly once the tank is installed (to the nearest mile)?
138)
A)
94 mi
B)
188 mi
C)
125 mi
D)
376 mi
Provide the proper response.
139)
A student knows that
a
f(x) dx diverges, but needs to investigate
a
g(x) dx , where
g(x) =f(x)
53 . Does this integral necessarily also diverge?
139)
A)
No
B)
Yes
Use integration by parts to find the integral.
140)
x 6 – x dx
140)
A)
–2
3x(6 – x)3/2 –4
15 (6 – x)5/2 + C
B)
–2
3x(6 – x)3/2 –2
5(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
Find the average value of the function on the given interval.
141)
f(x) =3x ln x ; [1, e2] Give your answer in exact form.
141)
A)
3
4
(3e2+ 1)
(e2– 1)
B)
3
4
(4e4+ 1)
(e2– 1)
C)
3
4
(3e4– 1)
(e2+ 1)
D)
3
4
(3e4+ 1)
(e2– 1)
Solve the problem. Round your answer to the nearest whole number.
142)
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 5%
compounded continuously.
142)
A)
$125,000
B)
$95,000
C)
$100,000
D)
$83,333
Solve the problem.
143)
A money market fund has a continuous flow of money at a rate of f(x) = 0.5x for 10 years. Find the
final amount if interest is earned at 8% compounded continuously.
143)
A)
$158.25
B)
$314.50
C)
$33.25
D)
$66.50
D)
Find the integral by using integration by parts or other techniques. Round the answer to four decimal places if necessary.
144)
12s3 ds
3– s4
144)
A)
–3
2 3 –s4
+ C
B)
6s4
3–s4
C)
–6 3 –s4+ C
D)
–6s33–s4+ C
D)
Find the volume of the solid of revolution formed by rotating about the x–axis the region bounded by the curves.
145)
f(x) = x2, y = 0, x = 1, x =23
145)
A)
1,287,268.6
B)
4055.33
C)
6,436,342
D)
1,287,268.4
D)
D)
Use integration by parts to find the integral. Round the answer to two decimal places if necessary.
146)
5
0
x3ln 2x dx
146)
A)
328.53
B)
398.84
C)
–153.95
D)
320.72
Use the table of integrals or a computer or calculator with symbolic integration capabilities to find the integral.
147)
dx
9x2+2x
147)
A)
1
9 ln 9x2+2x
B)
1
9ln 1
9x +2+ C
C)
1
2ln x
9x +2+ C
D)
1
9tan–1x
9+ C
Determine whether the improper integral is convergent or divergent.
148)
1
ln x dx
148)
A)
Divergent
B)
Convergent
Find the area between the graph of the function and the x–axis over the given interval, if possible.
149)
f(x) =7
(x – 1)2 for (–, 0]
149)
A)
–7
B)
1
C)
7
D)
Divergent
Find the average value of the function on the given interval.
150)
f(x) = 4 – x2; [1, 19]
150)
A)
–122.796
B)
–116.526
C)
–377
D)
–123.000
Determine whether the improper integral is convergent or divergent.
151)
–
x5e–x6 dx
151)
A)
Convergent
B)
Divergent
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.
152)
f(x) = 2000 at 2% compounded continuously
152)
A)
$27,042.19
B)
$22,140.28
C)
$100,000.00
D)
$222,140.28
Find the integral by using integration by parts or other techniques. Round the answer to four decimal places if necessary.
153)
2
0
x23x3+7 dx
153)
A)
5.9007
B)
4.2485
C)
9.2483
D)
7.7889
Determine whether the improper integral is convergent or divergent.
154)
5
dx
x8/3
154)
A)
Divergent
B)
Convergent
The function represents the rate of flow of money in dollars per year. Assume a 10–year period and find the present
value.
155)
f(x) =3000x –100x2 at 7% compounded continuously
155)
A)
$75,483.18
B)
$115,298.44
C)
$17,174.14
D)
$365,037.29
Answer Key
Testname: C8
Answer Key
Testname: C8
Answer Key
Testname: C8
Answer Key
Testname: C8