Deck 5: Integration
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Deck 5: Integration
1
Find the indefinite integral.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)


2
What is the average value of
on the closed interval
?
A)6.181
B)2.000
C)1.819
D)7.364


A)6.181
B)2.000
C)1.819
D)7.364
1.819
3
Find the indefinite integral.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)


4
The graph of
consists of line segments and quarter circles as shown in the graph to the right.What is the value of
? 
A)
B)
C)
D)



A)

B)

C)

D)

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5
Let R be the region between the function
the x-axis,and the lines
and
.Using the Trapezoidal Sum,compute the area when there are four equal subdivisions.
A)221
B)328
C)228
D)74



A)221
B)328
C)228
D)74
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6
Find the position of the particle at any time t if
cm/sec and
.


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7
Evaluate:
A)
B)
C)
D)

A)

B)

C)

D)

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8
If
is an even function and
is an odd function where
and
,find the value of
.
A)
B)
C)
D)





A)

B)

C)

D)

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9
On the closed interval [0,3],what is the velocity of the particle when its acceleration is at a maximum? Round your answer to three decimal places.
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10
What is
if
and
?
A)
B)
C)
D)



A)

B)

C)

D)

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11
At
,is the speed of the particle increasing or decreasing if
?
A)decreasing
B)increasing


A)decreasing
B)increasing
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12
What is the average value of
for the closed interval
?
A)
B)
C)
D)


A)

B)

C)

D)

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13
If
,what is
A)
B)
C)12
D)36


A)

B)

C)12
D)36
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14
If
and
,what is the value of
.
A)
B)
C)
D)



A)

B)

C)

D)

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15
Evaluate:
.
A)
B)
C)0
D)The function is not integrable on the interval
.

A)

B)

C)0
D)The function is not integrable on the interval

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16
The graph of
shown below consists of three line segments and one semicircle.Let
.Which of the following statements must be false?
A)
B)
C)
D)
has a relative maximum at




A)

B)

C)

D)


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17
The acceleration of a particle is given as
cm/sec2 on the closed interval [0,3] as illustrated on the graph shown.
![The acceleration of a particle is given as cm/sec<sup>2</sup> on the closed interval [0,3] as illustrated on the graph shown. Find the velocity of the particle at any time t if cm/sec.](https://storage.examlex.com/TB7497/11eac44f_ece7_dc6c_bedf_215fdace6437_TB7497_00.jpg)
Find the velocity of the particle at any time t if
cm/sec.
![The acceleration of a particle is given as cm/sec<sup>2</sup> on the closed interval [0,3] as illustrated on the graph shown. Find the velocity of the particle at any time t if cm/sec.](https://storage.examlex.com/TB7497/11eac44f_ece7_b55b_bedf_817fd5da4c24_TB7497_11.jpg)
![The acceleration of a particle is given as cm/sec<sup>2</sup> on the closed interval [0,3] as illustrated on the graph shown. Find the velocity of the particle at any time t if cm/sec.](https://storage.examlex.com/TB7497/11eac44f_ece7_dc6c_bedf_215fdace6437_TB7497_00.jpg)
Find the velocity of the particle at any time t if
![The acceleration of a particle is given as cm/sec<sup>2</sup> on the closed interval [0,3] as illustrated on the graph shown. Find the velocity of the particle at any time t if cm/sec.](https://storage.examlex.com/TB7497/11eac44f_ece7_dc6d_bedf_7b299084c790_TB7497_11.jpg)
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18
Find
if
.
A)
B)
C)
D)


A)

B)

C)

D)

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19
Evaluate
.
A)
B)
C)
D)

A)

B)

C)

D)

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20
Initially a water tank contains 150 ft3.Water begins to drain from the tank at the rate of
cubic feet per hour.How many cubic feet of water will remain in the tank after 2 hours? Round your answer to three decimal places.
A)24.805
B)125.195
C)97.470
D)52.530

A)24.805
B)125.195
C)97.470
D)52.530
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21
Evaluate the integral
.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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22
Find the integral
.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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23
Find
.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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24
Find the integral
.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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25
Find the area of the shaded region for the function
.
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)

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26
Evaluate the integral
.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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27
Find the area of the shaded region for the function
.
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)

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28
Find the area of the shaded region for the function
.
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)

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29
Find the indefinite integral.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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30
Use the differential equation
and the initial condition
to find y.
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)

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31
Find the integral
.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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32
Find the integral
.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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33
Use the differential equation
and the initial condition
to find y.
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)

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34
Find the indefinite integral.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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35
Find the indefinite integral.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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36
Find the indefinite integral.
A)
B)

C)
D)
E)

A)

B)


C)

D)

E)

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37
Find the indefinite integral.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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38
Find the indefinite integral.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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39
Find the indefinite integral
.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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40
Find the indefinite integral of
.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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41
Suppose a population of bacteria is changing at a rate of
,where t is the time in days.The initial population (when
)is 2,000.Identify an equation that gives the population at any time t and use it to find the population when
days.Round your answer to the nearest integer.
A)3,423
B)3,718
C)4,423
D)2,717
E)3,717



A)3,423
B)3,718
C)4,423
D)2,717
E)3,717
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42
Find the area of the region bounded by the graphs of the equations
,
,
,and
.Round your answer to four decimal places.
A)15.2661
B)16.5423
C)16.2661
D)17.5423
E)16.8755




A)15.2661
B)16.5423
C)16.2661
D)17.5423
E)16.8755
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43
Suppose a population of bacteria is changing at a rate of
,where t is the time in days.The initial population (when
)is 1,500.Write an equation that gives the population at any time t.
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)

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44
Evaluate the definite integral.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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45
Find the indefinite integral.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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46
Find
.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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47
Find
given
.
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)

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48
Find the indefinite integral
.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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49
Evaluate
.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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50
Find the indefinite integral.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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51
Find
if
.
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)

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52
Find
.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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53
Find the time required for an object to cool from 340°F to 240°F by evaluating
,where t is time in minutes.Round your answer to four decimal places.
A)7.3417 minutes
B)5.0489 minutes
C)4.2110 minutes
D)4.6321 minutes
E)6.6742 minutes

A)7.3417 minutes
B)5.0489 minutes
C)4.2110 minutes
D)4.6321 minutes
E)6.6742 minutes
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54
Find
.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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55
Find the area of the region given below bounded by the graph of
.
A)6
B)
C)
D)7
E)


A)6
B)

C)

D)7
E)

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56
Find the solution of the differential equation
which passes through the point
.
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)

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57
Evaluate the definite integral
.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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58
Find the solution of the differential equation
which passes through the point
.
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)

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59
Use integration to find the particular solution of the differential equation
which passes through the point
.
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)

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60
Suppose the demand equation for a product is
.Find the average price p on the interval
.Round your answer to the nearest dollar.
A)$42
B)$756
C)$832
D)$76
E)$69


A)$42
B)$756
C)$832
D)$76
E)$69
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61
Find the indefinite integral.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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62
Find the indefinite integral.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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63
Find the indefinite integral of the following function.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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64
Find the indefinite integral
.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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65
Find the indefinite integral of the following function.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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66
Solve the differential equation.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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67
Find the indefinite integral of the following function and check the result by differentiation.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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68
The rate of change in sales S is inversely proportional to time
measured in weeks.Find S as a function of t if sales after 2 and 4 weeks are 250 units and 450 units respectively.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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69
Find the indefinite integral of the following function and check the result by differentiation.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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70
Find the indefinite integral
.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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71
Find the indefinite integral of the following function and check the result by differentiation.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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72
Find the indefinite integral.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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73
Find the indefinite integral
.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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74
Find the indefinite integral.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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75
Find the indefinite integral
.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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76
Find the indefinite integral of the following function.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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77
Find the indefinite integral.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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78
Find the indefinite integral
.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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79
Solve the differential equation.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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80
Find the indefinite integral.
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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