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Deck 12: Integration and Its Applications
Full screen (f)
Question
Find the cost function for the marginal cost 
and fixed cost of 
(for x = 0).
A)
B)
C)
D)
E)
and fixed cost of (for x = 0).A)
B)
C)
D)
E)
Question
Use algebra to rewrite the integrand; then integrate and simplify. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Evaluate the integral 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Find the indefinite integral and check the result by differentiation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Question
Find the indefinite integral 
and check your result by differentiation.
A)
B)
C)
D)
E)
and check your result by differentiation.A)
B)
C)
D)
E)
Question
Identify u and 
for the integral 
.
A)
and 
B)
and 
C)
and 
D)
and 
E)
and 
for the integral .A)
and B)
and C)
and D)
and E)
and Question
Find the indefinite integral 
and check your result by differentiation.
A)
B)
C)4
D)
E)
and check your result by differentiation.A)
B)
C)4
D)
E)
Question
Find the particular solution that satisfies the differential equation 
and initial condition 
.
A)
B)
C)
D)
E)
and initial condition .A)
B)
C)
D)
E)
Question
Find the indefinite integral and check the result by differentiation. 
A)
B)
C)
D)
E)none of the above
A)
B)
C)
D)
E)none of the above
Question
Identify 
and 
for the integral 
.
A)
and 
B)
and 
C)
and 
D)
and 
E)
and 
and for the integral .A)
and B)
and C)
and D)
and E)
and Question
Evaluate the integral 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Evaluate the integral 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
An evergreen nursery sells a certain shrub after 4 years. The growth rate of the shrub is given by 
, where t is the time in years and h is the height in centimeters. The seedlings are 10 centimeters tall when planted (t = 0). How tall are the shrubs when they are sold?
A)36 centimeters
B)40 centimeters
C)44 centimeters
D)54 centimeters
E)70 centimeters
, where t is the time in years and h is the height in centimeters. The seedlings are 10 centimeters tall when planted (t = 0). How tall are the shrubs when they are sold?A)36 centimeters
B)40 centimeters
C)44 centimeters
D)54 centimeters
E)70 centimeters
Question
Evaluate the integral 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Evaluate the integral 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find a function that satisfies the conditions 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Evaluate the integral 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
The graph of the derivative of a function is given below. Sketch the graphs of two functions that have the given derivative. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the indefinite integral of the following function and check the result by differentiation. 
A)
B)
C)
D)
E)none of the above
A)
B)
C)
D)
E)none of the above
Question
Find the equation of the function f whose graph passes through the point 
and whose derivative is 
.
A)
B)
C)
D)
E)
and whose derivative is .A)
B)
C)
D)
E)
Question
Find the indefinite integral of the following function and check the result by differentiation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the indefinite integral. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Evaluate the integral 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the indefinite integral. 
A)
B)
C)
D)integral does not exist
E)none of the above
A)
B)
C)
D)integral does not exist
E)none of the above
Question
Find the indefinite integral. 
A)
B)
C)
D)
E)none of the above
A)
B)
C)
D)
E)none of the above
Question
Evaluate the integral 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use formal substitution to find the indefinite integral 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Find the indefinite integral of the following function and check the result by differentiation. 
A)
B)
C)
D)
E)none of the above
A)
B)
C)
D)
E)none of the above
Question
Use the Log Rule to find the indefinite integral for 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Evaluate the integral 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the indefinite integral of the following function and check the result by differentiation. 
A)
B)
C)
D)
E)none of the above
A)
B)
C)
D)
E)none of the above
Question
Find the indefinite integral. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the supply function 
that satisfies 
and the initial condition x = 700 when 
.
A)
B)
C)
D)
E)
that satisfies and the initial condition x = 700 when .A)
B)
C)
D)
E)
Question
Evaluate the integral 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
The marginal cost of a product is modeled by 
, when x = 8, C = 40. Find the cost function.
A)
B)
C)
D)
E)
, when x = 8, C = 40. Find the cost function.A)
B)
C)
D)
E)
Question
Find the indefinite integral. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the indefinite integral of the following function and check the result by differentiation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Evaluate the integral 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the indefinite integral. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Sketch the region whose area is given by the definite integral and then use a geometric formula to evaluate the integral. 
A)
B)
C)
D)
E)none of the above
A)
B)
C)
D)
E)none of the above
Question
Find the area of the region bounded by the graphs of the algebraic functions. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use any basic integration formula or formulas to find the indefinite integral 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Find the area between the curve 
and the x-axis from 
.
A)
B)
C)
D)
E)
and the x-axis from .A)
B)
C)
D)
E)
Question
Set up the definite integral that gives the area of the region bounded by the graphs. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the average value of the function over the given interval. ![<strong>Find the average value of the function over the given interval. on [0,8]</strong> A) B) C) D) E) <div style=padding-top: 35px>](https://storage.examlex.com/TB8692/11eb99ec_11f9_1500_bdc5_33b94cdb1dd4_TB8692_11.jpg)
on [0,8]
A)![<strong>Find the average value of the function over the given interval. on [0,8]</strong> A) B) C) D) E) <div style=padding-top: 35px>](https://storage.examlex.com/TB8692/11eb99ec_11f9_1501_bdc5_b9b52cb53545_TB8692_11.jpg)
B)![<strong>Find the average value of the function over the given interval. on [0,8]</strong> A) B) C) D) E) <div style=padding-top: 35px>](https://storage.examlex.com/TB8692/11eb99ec_11f9_3c12_bdc5_0100fc72a112_TB8692_11.jpg)
C)![<strong>Find the average value of the function over the given interval. on [0,8]</strong> A) B) C) D) E) <div style=padding-top: 35px>](https://storage.examlex.com/TB8692/11eb99ec_11f9_3c13_bdc5_219d17bcdee5_TB8692_11.jpg)
D)![<strong>Find the average value of the function over the given interval. on [0,8]</strong> A) B) C) D) E) <div style=padding-top: 35px>](https://storage.examlex.com/TB8692/11eb99ec_11f9_3c14_bdc5_87333e2d0f58_TB8692_11.jpg)
E)![<strong>Find the average value of the function over the given interval. on [0,8]</strong> A) B) C) D) E) <div style=padding-top: 35px>](https://storage.examlex.com/TB8692/11eb99ec_11f9_3c15_bdc5_592e90ca76c2_TB8692_11.jpg)
on [0,8]A)
B)
C)
D)
E)
Question
Evaluate the following definite integral. 
Use a graphing utility to check your answer.
A)
B)
C)
D)
E)
Use a graphing utility to check your answer.A)
B)
C)
D)
E)
Question
Determine the area of the given region. 
A)
B)
C)
D)
E)None of the above
A)
B)
C)
D)
E)None of the above
Question
Find the area of the region bounded by the graphs of the algebraic functions. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
The rate of depreciation of a building is given by 
dollars per year, 
Use the definite integral to find the total depreciation over the first 
years.
A)
B)
C)
D)
E)
dollars per year, Use the definite integral to find the total depreciation over the first years.A)
B)
C)
D)
E)
Question
Determine the graph whose area (the shaded region) is represented by the integral. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the average value of the function over the given interval. ![<strong>Find the average value of the function over the given interval. on [-3,3]</strong> A)6 B)21 C)36 D)4 E)20 <div style=padding-top: 35px>](https://storage.examlex.com/TB8692/11eb99ec_11f9_14ff_bdc5_7dc2ef9f6152_TB8692_11.jpg)
on [-3,3]
A)6
B)21
C)36
D)4
E)20
on [-3,3]A)6
B)21
C)36
D)4
E)20
Question
Sketch the region whose area is given by the definite integral and then use a geometric formula to evaluate the integral. 
A)-145
B)290
C)200
D)100
E)10
A)-145
B)290
C)200
D)100
E)10
Question
The integrand of the following definite integral is a difference of two functions. 
Sketch the graph of the two functions and shade the region whose area is represented by the integral.
A)
B)
C)
D)
E)
Sketch the graph of the two functions and shade the region whose area is represented by the integral.A)
B)
C)
D)
E)
Question
Evaluate the definite integral of the algebraic function. 
Use a graphing utility to verify your results.
A)-12
B)-56
C)-36
D)8
E)-28
Use a graphing utility to verify your results.A)-12
B)-56
C)-36
D)8
E)-28
Question
Find the area of the shaded region. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use the values 
and 
to evaluate the definite integral 
.
A)14
B)2
C)5
D)11
E)4
and to evaluate the definite integral .A)14
B)2
C)5
D)11
E)4
Question
Find the equation of the function whose derivative is 
and whose graph passes through the point 
.
A)
B)
C)
D)
E)
and whose graph passes through the point .A)
B)
C)
D)
E)
Question
Evaluate the definite integral 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Evaluate the definite integral of the algebraic function. 
Use a graphing utility to verify your results.
A)18.4007
B)29.6329
C)59.5941
D)38.9974
E)48.0336
Use a graphing utility to verify your results.A)18.4007
B)29.6329
C)59.5941
D)38.9974
E)48.0336
Question
Estimate the surface area of the pond shown in the figure using the Midpoint Rule. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use the Midpoint Rule with n = 4 to approximate the area of the following region. 
A)1.156
B)1.324
C)1.575
D)1.275
E)1.876
A)1.156
B)1.324
C)1.575
D)1.275
E)1.876
Question
The demand function for a product is 
, where p is the number of dollars and x is the number of units. If the equilibrium price is 
, what is the consumer's surplus?
A)$
B)$
C)$
D)$
E)$
, where p is the number of dollars and x is the number of units. If the equilibrium price is , what is the consumer's surplus?A)$
B)$
C)$
D)$
E)$
Question
Use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the graph of ![<strong>Use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the graph of and the x-axis over the interval [ ].</strong> A)11.4421 B)11.0023 C)11.2114 D)11.0000 E)12.0000 <div style=padding-top: 35px>](https://storage.examlex.com/TB8692/11eb99ec_11fb_3737_bdc5_99b0948d346e_TB8692_11.jpg)
and the x-axis over the interval [ ![<strong>Use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the graph of and the x-axis over the interval [ ].</strong> A)11.4421 B)11.0023 C)11.2114 D)11.0000 E)12.0000 <div style=padding-top: 35px>](https://storage.examlex.com/TB8692/11eb99ec_11fb_3738_bdc5_8d2d8647df6b_TB8692_11.jpg)
].
A)11.4421
B)11.0023
C)11.2114
D)11.0000
E)12.0000
and the x-axis over the interval [ ].A)11.4421
B)11.0023
C)11.2114
D)11.0000
E)12.0000
Question
The revenue from a manufacturing process (in millions of dollars per year) is projected to follow the model 
for 10 years. Over the same period of time, the cost (in millions of dollars per year) is projected to follow the model 
, where t is the time (in years). Approximate the profit over the 10-year period, beginning with t = 0. Round your answer to two decimal places.
A)
million
B)
million
C)
million
D)
million
E)
million
for 10 years. Over the same period of time, the cost (in millions of dollars per year) is projected to follow the model , where t is the time (in years). Approximate the profit over the 10-year period, beginning with t = 0. Round your answer to two decimal places.A)
millionB)
millionC)
millionD)
millionE)
million Question
Use the Midpoint Rule n = 4 to approximate the area of the following region. 
A)2.5
B)1.2
C)1.5
D)1.9
E)2.3
A)2.5
B)1.2
C)1.5
D)1.9
E)2.3
Question
Estimate the surface area of the oil spill shown in the figure using the Midpoint Rule. 
A)
481.6 
B)
301.6 
C)
311.6 
D)
431.6 
E)
381.6 
A)
481.6 B)
301.6 C)
311.6 D)
431.6 E)
381.6 Question
Use the Midpoint Rule with 
to approximate the area of the region bounded by the graph of and the -axis over the interval. Sketch the region. 
A)The approximate area is:
B)The approximate area is:
C)The approximate area is:
D)The approximate area is:
E)The approximate area is:
to approximate the area of the region bounded by the graph of and the -axis over the interval. Sketch the region. A)The approximate area is:
B)The approximate area is:
C)The approximate area is:
D)The approximate area is:
E)The approximate area is:
Question
Use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the graph of ![<strong>Use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the graph of and the x-axis over the interval [0,1].</strong> A)1.7524 B)1.3126 C)1.5217 D)2.3103 E)1.3103 <div style=padding-top: 35px>](https://storage.examlex.com/TB8692/11eb99ec_11fb_5e49_bdc5_af211091ac23_TB8692_11.jpg)
and the x-axis over the interval [0,1].
A)1.7524
B)1.3126
C)1.5217
D)2.3103
E)1.3103
and the x-axis over the interval [0,1].A)1.7524
B)1.3126
C)1.5217
D)2.3103
E)1.3103
Question
Two models, 
and 
, are given for revenue (in billions of dollars per year) for a large corporation. Both models are estimates of revenues for 2007 through 2011, with t = 7 corresponding to 2007. Which model is projecting the greater revenue? How much more total revenue does that model project over the five-year period?
A)The model
projects greater revenue than 
. 
billion
B)The model
projects greater revenue than 
. 
billion
C)The model
projects greater revenue than 
. 
billion
D)The model
projects greater revenue than 
. 
billion
E)The model
projects greater revenue than 
. 
billion
and , are given for revenue (in billions of dollars per year) for a large corporation. Both models are estimates of revenues for 2007 through 2011, with t = 7 corresponding to 2007. Which model is projecting the greater revenue? How much more total revenue does that model project over the five-year period?A)The model
projects greater revenue than . billionB)The model
projects greater revenue than . billionC)The model
projects greater revenue than . billionD)The model
projects greater revenue than . billionE)The model
projects greater revenue than . billion Question
Find the consumer and producer surpluses by using the demand and supply functions, where p is the price (in dollars) and x is the number of units (in millions). 
A)a. $2587.50b. $3725.00
B)a. $5587.50b. $4725.00
C)a. $2587.50b. $1725.00
D)a. $1587.50b. $4725.00
E)a. $3587.50b. $4725.00
A)a. $2587.50b. $3725.00
B)a. $5587.50b. $4725.00
C)a. $2587.50b. $1725.00
D)a. $1587.50b. $4725.00
E)a. $3587.50b. $4725.00
Question
Estimate the surface area of the golf green shown in the figure using the midpoint rule. 
A)966
B)161
C)1449
D)1550
E)234
A)966
B)161
C)1449
D)1550
E)234
Question
Use the Midpoint Rule with 
to approximate 
where 
. Then use a graphing utility to evaluate the definite integral. Compare your results.
A)a. Midpoint Rule:
b. Graphing utility: 
B)a. Midpoint Rule:
b. Graphing utility: 
C)a. Midpoint Rule:
b. Graphing utility: 
D)a. Midpoint Rule:
b. Graphing utility: 
E)a. Midpoint Rule:
b. Graphing utility: 
to approximate where . Then use a graphing utility to evaluate the definite integral. Compare your results.A)a. Midpoint Rule:
b. Graphing utility: B)a. Midpoint Rule:
b. Graphing utility: C)a. Midpoint Rule:
b. Graphing utility: D)a. Midpoint Rule:
b. Graphing utility: E)a. Midpoint Rule:
b. Graphing utility: Question
Use the rectangles to approximate the area of the region. Compare your result with the exact area obtained with a definite integral. 
A)a. The approximate area: 3b. The exact area: 2
B)a. The approximate area: 2b. The exact area: 3
C)a. The approximate area: 2b. The exact area: 1
D)a. The approximate area: 2b. The exact area: 2
E)a. The approximate area: 1b. The exact area: 2
A)a. The approximate area: 3b. The exact area: 2
B)a. The approximate area: 2b. The exact area: 3
C)a. The approximate area: 2b. The exact area: 1
D)a. The approximate area: 2b. The exact area: 2
E)a. The approximate area: 1b. The exact area: 2
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Deck 12: Integration and Its Applications
1
Find the cost function for the marginal cost and fixed cost of (for x = 0).
A)
B)
C)
D)
E)
and fixed cost of (for x = 0).A)
B)
C)
D)
E)
2
Use algebra to rewrite the integrand; then integrate and simplify.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
3
Evaluate the integral .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
4
Find the indefinite integral and check the result by differentiation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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5
A ball is thrown vertically upwards from a height of 10 ft with an initial velocity of 70 ft per second. How high will the ball go?
A)239.6875 ft
B)67.4219 ft
C)86.5625 ft
D)219.6875 ft
E)241.6875 ft
A)239.6875 ft
B)67.4219 ft
C)86.5625 ft
D)219.6875 ft
E)241.6875 ft
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6
Find the indefinite integral and check your result by differentiation.
A)
B)
C)
D)
E)
and check your result by differentiation.A)
B)
C)
D)
E)
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7
Identify u and for the integral .
A) and
B) and
C) and
D) and
E) and
for the integral .A)
and B)
and C)
and D)
and E)
and Unlock Deck
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8
Find the indefinite integral and check your result by differentiation.
A)
B)
C)4
D)
E)
and check your result by differentiation.A)
B)
C)4
D)
E)
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9
Find the particular solution that satisfies the differential equation and initial condition .
A)
B)
C)
D)
E)
and initial condition .A)
B)
C)
D)
E)
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10
Find the indefinite integral and check the result by differentiation.
A)
B)
C)
D)
E)none of the above
A)
B)
C)
D)
E)none of the above
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11
Identify and for the integral .
A) and
B) and
C) and
D) and
E) and
and for the integral .A)
and B)
and C)
and D)
and E)
and Unlock Deck
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12
Evaluate the integral .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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13
Evaluate the integral .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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14
An evergreen nursery sells a certain shrub after 4 years. The growth rate of the shrub is given by , where t is the time in years and h is the height in centimeters. The seedlings are 10 centimeters tall when planted (t = 0). How tall are the shrubs when they are sold?
A)36 centimeters
B)40 centimeters
C)44 centimeters
D)54 centimeters
E)70 centimeters
, where t is the time in years and h is the height in centimeters. The seedlings are 10 centimeters tall when planted (t = 0). How tall are the shrubs when they are sold?A)36 centimeters
B)40 centimeters
C)44 centimeters
D)54 centimeters
E)70 centimeters
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15
Evaluate the integral .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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16
Evaluate the integral
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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17
Find a function that satisfies the conditions .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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18
Evaluate the integral .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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19
The graph of the derivative of a function is given below. Sketch the graphs of two functions that have the given derivative.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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20
Find the indefinite integral of the following function and check the result by differentiation.
A)
B)
C)
D)
E)none of the above
A)
B)
C)
D)
E)none of the above
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21
Find the equation of the function f whose graph passes through the point and whose derivative is .
A)
B)
C)
D)
E)
and whose derivative is .A)
B)
C)
D)
E)
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22
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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23
Find the indefinite integral.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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24
Evaluate the integral
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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25
Find the indefinite integral.
A)
B)
C)
D)integral does not exist
E)none of the above
A)
B)
C)
D)integral does not exist
E)none of the above
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26
Find the indefinite integral.
A)
B)
C)
D)
E)none of the above
A)
B)
C)
D)
E)none of the above
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27
Evaluate the integral
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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28
Use formal substitution to find the indefinite integral .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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29
Find the indefinite integral of the following function and check the result by differentiation.
A)
B)
C)
D)
E)none of the above
A)
B)
C)
D)
E)none of the above
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30
Use the Log Rule to find the indefinite integral for .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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31
Evaluate the integral
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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32
Find the indefinite integral of the following function and check the result by differentiation.
A)
B)
C)
D)
E)none of the above
A)
B)
C)
D)
E)none of the above
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33
Find the indefinite integral.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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34
Find the supply function that satisfies and the initial condition x = 700 when .
A)
B)
C)
D)
E)
that satisfies and the initial condition x = 700 when .A)
B)
C)
D)
E)
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35
Evaluate the integral
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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36
The marginal cost of a product is modeled by , when x = 8, C = 40. Find the cost function.
A)
B)
C)
D)
E)
, when x = 8, C = 40. Find the cost function.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 of the following function and check the result by differentiation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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39
Evaluate the integral
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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40
Find the indefinite integral.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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41
Sketch the region whose area is given by the definite integral and then use a geometric formula to evaluate the integral.
A)
B)
C)
D)
E)none of the above
A)
B)
C)
D)
E)none of the above
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42
Find the area of the region bounded by the graphs of the algebraic functions.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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43
Use any basic integration formula or formulas to find the indefinite integral .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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44
Find the area between the curve and the x-axis from .
A)
B)
C)
D)
E)
and the x-axis from .A)
B)
C)
D)
E)
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45
Set up the definite integral that gives the area of the region bounded by the graphs.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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46
Find the average value of the function over the given interval. on [0,8]
A)
B)
C)
D)
E)
on [0,8]A)
B)
C)
D)
E)
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47
Evaluate the following definite integral. Use a graphing utility to check your answer.
A)
B)
C)
D)
E)
Use a graphing utility to check your answer.A)
B)
C)
D)
E)
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48
Determine the area of the given region.
A)
B)
C)
D)
E)None of the above
A)
B)
C)
D)
E)None of the above
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49
Find the area of the region bounded by the graphs of the algebraic functions.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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50
The rate of depreciation of a building is given by dollars per year, Use the definite integral to find the total depreciation over the first years.
A)
B)
C)
D)
E)
dollars per year, Use the definite integral to find the total depreciation over the first years.A)
B)
C)
D)
E)
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51
Determine the graph whose area (the shaded region) is represented by the integral.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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52
Find the average value of the function over the given interval. on [-3,3]
A)6
B)21
C)36
D)4
E)20
on [-3,3]A)6
B)21
C)36
D)4
E)20
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53
Sketch the region whose area is given by the definite integral and then use a geometric formula to evaluate the integral.
A)-145
B)290
C)200
D)100
E)10
A)-145
B)290
C)200
D)100
E)10
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54
The integrand of the following definite integral is a difference of two functions. Sketch the graph of the two functions and shade the region whose area is represented by the integral.
A)
B)
C)
D)
E)
Sketch the graph of the two functions and shade the region whose area is represented by the integral.A)
B)
C)
D)
E)
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55
Evaluate the definite integral of the algebraic function. Use a graphing utility to verify your results.
A)-12
B)-56
C)-36
D)8
E)-28
Use a graphing utility to verify your results.A)-12
B)-56
C)-36
D)8
E)-28
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56
Find the area of the shaded region.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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57
Use the values and to evaluate the definite integral .
A)14
B)2
C)5
D)11
E)4
and to evaluate the definite integral .A)14
B)2
C)5
D)11
E)4
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58
Find the equation of the function whose derivative is and whose graph passes through the point .
A)
B)
C)
D)
E)
and whose graph passes through the point .A)
B)
C)
D)
E)
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59
Evaluate the definite integral .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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k this deck
60
Evaluate the definite integral of the algebraic function. Use a graphing utility to verify your results.
A)18.4007
B)29.6329
C)59.5941
D)38.9974
E)48.0336
Use a graphing utility to verify your results.A)18.4007
B)29.6329
C)59.5941
D)38.9974
E)48.0336
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61
Estimate the surface area of the pond shown in the figure using the Midpoint Rule.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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62
Use the Midpoint Rule with n = 4 to approximate the area of the following region.
A)1.156
B)1.324
C)1.575
D)1.275
E)1.876
A)1.156
B)1.324
C)1.575
D)1.275
E)1.876
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k this deck
63
The demand function for a product is , where p is the number of dollars and x is the number of units. If the equilibrium price is , what is the consumer's surplus?
A)$
B)$
C)$
D)$
E)$
, where p is the number of dollars and x is the number of units. If the equilibrium price is , what is the consumer's surplus?A)$
B)$
C)$
D)$
E)$
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64
Use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the graph of and the x-axis over the interval [ ].
A)11.4421
B)11.0023
C)11.2114
D)11.0000
E)12.0000
and the x-axis over the interval [ ].A)11.4421
B)11.0023
C)11.2114
D)11.0000
E)12.0000
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65
The revenue from a manufacturing process (in millions of dollars per year) is projected to follow the model for 10 years. Over the same period of time, the cost (in millions of dollars per year) is projected to follow the model , where t is the time (in years). Approximate the profit over the 10-year period, beginning with t = 0. Round your answer to two decimal places.
A) million
B) million
C) million
D) million
E) million
for 10 years. Over the same period of time, the cost (in millions of dollars per year) is projected to follow the model , where t is the time (in years). Approximate the profit over the 10-year period, beginning with t = 0. Round your answer to two decimal places.A)
millionB)
millionC)
millionD)
millionE)
million Unlock Deck
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66
Use the Midpoint Rule n = 4 to approximate the area of the following region.
A)2.5
B)1.2
C)1.5
D)1.9
E)2.3
A)2.5
B)1.2
C)1.5
D)1.9
E)2.3
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67
Estimate the surface area of the oil spill shown in the figure using the Midpoint Rule.
A) 481.6
B) 301.6
C) 311.6
D) 431.6
E) 381.6
A)
481.6 B)
301.6 C)
311.6 D)
431.6 E)
381.6 Unlock Deck
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68
Use the Midpoint Rule with to approximate the area of the region bounded by the graph of and the -axis over the interval. Sketch the region.
A)The approximate area is:
B)The approximate area is:
C)The approximate area is:
D)The approximate area is:
E)The approximate area is:
to approximate the area of the region bounded by the graph of and the -axis over the interval. Sketch the region. A)The approximate area is:
B)The approximate area is:
C)The approximate area is:
D)The approximate area is:
E)The approximate area is:
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69
Use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the graph of and the x-axis over the interval [0,1].
A)1.7524
B)1.3126
C)1.5217
D)2.3103
E)1.3103
and the x-axis over the interval [0,1].A)1.7524
B)1.3126
C)1.5217
D)2.3103
E)1.3103
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70
Two models, and , are given for revenue (in billions of dollars per year) for a large corporation. Both models are estimates of revenues for 2007 through 2011, with t = 7 corresponding to 2007. Which model is projecting the greater revenue? How much more total revenue does that model project over the five-year period?
A)The model projects greater revenue than . billion
B)The model projects greater revenue than . billion
C)The model projects greater revenue than . billion
D)The model projects greater revenue than . billion
E)The model projects greater revenue than . billion
and , are given for revenue (in billions of dollars per year) for a large corporation. Both models are estimates of revenues for 2007 through 2011, with t = 7 corresponding to 2007. Which model is projecting the greater revenue? How much more total revenue does that model project over the five-year period?A)The model
projects greater revenue than . billionB)The model
projects greater revenue than . billionC)The model
projects greater revenue than . billionD)The model
projects greater revenue than . billionE)The model
projects greater revenue than . billion Unlock Deck
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71
Find the consumer and producer surpluses by using the demand and supply functions, where p is the price (in dollars) and x is the number of units (in millions).
A)a. $2587.50b. $3725.00
B)a. $5587.50b. $4725.00
C)a. $2587.50b. $1725.00
D)a. $1587.50b. $4725.00
E)a. $3587.50b. $4725.00
A)a. $2587.50b. $3725.00
B)a. $5587.50b. $4725.00
C)a. $2587.50b. $1725.00
D)a. $1587.50b. $4725.00
E)a. $3587.50b. $4725.00
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72
Estimate the surface area of the golf green shown in the figure using the midpoint rule.
A)966
B)161
C)1449
D)1550
E)234
A)966
B)161
C)1449
D)1550
E)234
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73
Use the Midpoint Rule with to approximate where . Then use a graphing utility to evaluate the definite integral. Compare your results.
A)a. Midpoint Rule: b. Graphing utility:
B)a. Midpoint Rule: b. Graphing utility:
C)a. Midpoint Rule: b. Graphing utility:
D)a. Midpoint Rule: b. Graphing utility:
E)a. Midpoint Rule: b. Graphing utility:
to approximate where . Then use a graphing utility to evaluate the definite integral. Compare your results.A)a. Midpoint Rule:
b. Graphing utility: B)a. Midpoint Rule:
b. Graphing utility: C)a. Midpoint Rule:
b. Graphing utility: D)a. Midpoint Rule:
b. Graphing utility: E)a. Midpoint Rule:
b. Graphing utility: Unlock Deck
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74
Use the rectangles to approximate the area of the region. Compare your result with the exact area obtained with a definite integral.
A)a. The approximate area: 3b. The exact area: 2
B)a. The approximate area: 2b. The exact area: 3
C)a. The approximate area: 2b. The exact area: 1
D)a. The approximate area: 2b. The exact area: 2
E)a. The approximate area: 1b. The exact area: 2
A)a. The approximate area: 3b. The exact area: 2
B)a. The approximate area: 2b. The exact area: 3
C)a. The approximate area: 2b. The exact area: 1
D)a. The approximate area: 2b. The exact area: 2
E)a. The approximate area: 1b. The exact area: 2
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Unlock Deck
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