Deck 6: The Integral

Question 1

Evaluate the integral.

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E)

Answer 1

Question 2

Evaluate the integral.

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D)
E)

Answer 2

Question 3

Evaluate the integral.

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D)
E)

Answer 3

Question 4

Evaluate the integral.

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D)
E)

Question 5

Evaluate the integral.

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E)

Question 6

Evaluate the integral.

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E)

Question 7

Evaluate the integral.

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Question 8

Find if and the tangent line at has slope .

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E)

Question 10

Your name is Francesca Dragonetti (an assistant of Galileo Galilei)and, to impress your boss, you toss a weight upward at feet per second from the top of the Leaning Tower of Pisa (height 185 ft). Neglecting air resistance, find the weight s velocity and the height of the weight above the ground as a functions of time in seconds.

A) ,
B) ,
C) ,
D) ,
E) ,

Question 11

Evaluate the integral.

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Question 12

Evaluate the integral.

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E)

Question 14

Evaluate the integral mentally.

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Question 16

The velocity of a particle moving in a straight line is given by . Find an expression for the position after a time .

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D)
E)

Question 17

Find if and the tangent line at has slope .

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D)
E)

Question 18

The marginal cost of producing the box of computer disks is and the fixed cost is $150,000. Find the cost function

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B)
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D)
E)

Question 20

Evaluate the integral.

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D)
E)

Question 21

Evaluate the integral.

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E)

Question 22

Evaluate the integral.

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Question 23

Evaluate the integral.

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Question 24

Evaluate the integral.

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Question 25

Evaluate the integral.

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Question 26

Evaluate the given integral using the substitution.

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Question 27

A car traveling down a road has a velocity of mph at time hours. Find the total distance it travels from time hours to time hours. (Round your answer to the nearest mile.)

A)210 miles
B)224 miles
C)216 miles
D)206 miles
E)218 miles

Question 28

Evaluate the integral.

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B)
C)
D)
E)

Question 29

Find if and the tangent line at has the slope

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B)
C)
D)
E)

Question 30

Evaluate the integral.

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D)
E)

Question 31

Evaluate the integral.

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Question 32

Evaluate the integral.

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Question 33

Decide on what substitution to use, and then evaluate the given integral using a substitution.

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Question 34

Evaluate the integral. Please express your answer in terms of e .

Question 35

Evaluate the integral.

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Question 36

Evaluate the integral.

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E)

Question 37

Evaluate the integral.

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E)

Question 38

Evaluate the integral.

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Question 39

Evaluate the integral.

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E)

Question 40

Evaluate the integral.

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D)
E)

Question 41

Find if and the tangent line at ( x , f ( x ))has the slope.

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Question 42

Calculate the Riemann Sum for the integral using n = 4. Round to the nearest tenth.

A)981.1
B)1,297.5
C)519.0
D)648.8
E)1,217.1

Question 43

Calculate the Riemann Sum for the integral using n = 10. Round the answer to four decimal places.

A)63.0411
B)515.0749
C)51.5075
D)63.8522
E)64.6632

Question 44

The marginal cost of producing the x th roll of film is given by . The total cost to produce one roll is $1,000. Find the total cost function C ( x ).

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Question 45

The graph of the derivative of is shown. Compute the total change of over the interval .

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Question 46

The marginal cost function for the manufacture of portable CD players is given by where is the number of CD players manufactured. Use a Riemann sun with n = 15 to estimate the cost of producing the first 15 CD players.

A)$147.75
B)$148.95
C)$147.90
D)$133.88
E)$148.80

Question 47

Calculate the left Riemann sums for the function over the given interval, using the given values of . (When rounding, round answers to four decimal places.) over ,

A)Left sum = 65.4023
B)Left sum = 588.6211
C)Left sum = 19.4597
D)Left sum = 117.7242
E)Left sum = 11.7724

Question 48

Evaluate the integral.

Question 49

Calculate the Riemann Sum for the integral using n = 5.

A)156.19
B)7.78
C)23.33
D)468.57
E)148.41

Question 50

A race car has a velocity of ft/s seconds after starting. Use a Riemann sum with n = 10 to estimate how far the car travels in the first 5 seconds. (Round your answer to the nearest whole number.)

A)2,998 feet
B)800 feet
C)3,674 feet
D)3,550 feet
E)3,274 feet

Question 51

The velocity of a particle moving in a straight line is given by . Given that the distance s = 0 at t = 0, find an expression for s in terms of t without any unknown constants.

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E)

Question 52

The rate of change of the total number, in thousand of articles, of research articles in the prominent journal Physics Review written by researchers in Europe is shown in the graph, where t is time in years represents the start of 1987). Use both left and right Riemann sums with 7 subdivisions to estimate the total number of articles in Physics Review written by researchers in Europe in the 14-year period beginning 1987. (Estimate each value of to the nearest 0.5). Use the sums to obtain an estimate of .

A)60,000 articles
B)52,000 articles
C)8,000 articles
D)56,000 articles
E)4,000 articles

Question 53

Calculate the left Riemann sums for the function over the given interval, using the given values of . (When rounding, round answers to four decimal places.) over ,

A)Left sum = 0.3548
B)Left sum = 0.7095
C)Left sum = 8.8688
D)Left sum = 1.7738
E)Left sum = 1.4190

Question 54

Use the given graph to estimate the left Riemann sum for the given interval with the stated number of subdivisions.

A)Left Sum = 1
B)Left Sum = - 1
C)Left Sum = 2
D)Left Sum = - 2
E)Left Sum = 0

Question 55

A model rocket has upward velocity seconds after launch. Use a Riemann sum with n = 10 to estimate how high the rocket is 2 seconds after launch.

A)184.8 feet
B)158.4 feet
C)136.8 feet
D)115.2 feet
E)240 feet

Question 56

Calculate the left Riemann sum for the function over the given interval using the given values of . over ,

A)Left Sum = 5
B)Left Sum = - 5
C)Left Sum = 7
D)Left Sum = 4
E)Left Sum = - 4

Question 57

Calculate the Riemann Sum for the integral using n = 5. Give the answer correct to two decimal places.

A)0.98
B)0.38
C)0.84
D)0.69
E)0.89

Question 58

The normal distribution curve which models, distributions of data in a wide range of applications, is given by the function where and and are constants called the standard deviation and the mean, respectively. Its graph is shown in the figure. In a survey, consumers were asked to rate a new toothpaste on a scale of 1-10. The resulting data are modeled by a normal distribution with and . The percentage of consumers who gave the toothpaste a score between a and b on the section is given by . Use a Riemann sum with n = 10 to estimate the percentage of customers who rated the toothpaste 4 or higher. (Use the range 3.5 to 10.5.)

A)88%
B)92%
C)89%
D)90%
E)91%

Question 59

Calculate the Riemann Sum for the integral using n = 4.

A)14
B)6
C)16
D)8
E)10

Question 60

The velocity of a particle moving in a straight line is given by Find an expression for the position after time .

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B)
C)
D)
E)

Question 61

Evaluate the integral.

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Question 62

The oxygen consumption of a bird embryo increases from the time the egg is laid through the time the chick hatches. In a typical galliform bird, the oxygen consumption, in milliliters per hour, can be approximated by where t is time (in days)since the egg was laid. (An egg will typically hatch at around t = 28.)Find the total amount of oxygen consumed during the ninth and tenth days ( t = 8 to t = 10).

A)47
B)457
C)61
D)17
E)1,131

Question 63

Evaluate the integral.

A)2,976
B)1,152
C)2,400
D)4,704
E)1,248

Question 64

Evaluate the integral.

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Question 65

Evaluate the integral.

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Question 66

The way Professor Waner drives, he burns gas at the rate of gallons each hour, hours after a fill-up. Find the number of gallons of gas he burns in the first hours after a fill-up. Please round the answer to the nearest gallon.

A)14 gallons
B)16 gallons
C)11 gallons
D)17 gallons
E)13 gallons

Question 67

Calculate the Riemann Sum for the integral using n = 4.

Question 68

Evaluate the integral.

A)11
B)108
C)152
D)200
E)47

Question 69

Calculate the total area of the region bounded by the line , the , and the lines and

A)5,200
B)200
C)100
D)53,200
E)2,600

Question 70

Evaluate the integral.

A)30 ( ln 204 + ln 15 )
B)45 ( ln 15 - ln 204 )
C)22.5 ( ln 204 + ln 15 )
D)22.5 ( ln 204 - ln 15 )
E)15 ( ln 204 - ln 15 )

Question 71

Calculate the total area of the region bounded by the line , the and the lines and

A)387
B)4,185
C)4,603
D)4,347
E)12,879