Deck 5: Integration

Question 1

Use a finite sum to estimate the average value of the function on the given interval by partitioning the interval and
evaluating the function at the midpoints of the subintervals.

Answer 1

D

Question 2

f(x) = x2 between x = 0 and x = 1 using the "midpoint rule" with two rectangles of equal width.

A) )3145
B) )625
C) )75
D) )125

Answer 2

A

Question 3

Use a finite sum to estimate the average value of the function on the given interval by partitioning the interval and
evaluating the function at the midpoints of the subintervals.

Answer 3

D

Question 4

Use a finite sum to estimate the average value of the function on the given interval by partitioning the interval and
evaluating the function at the midpoints of the subintervals.

Question 5

Use a finite sum to estimate the average value of the function on the given interval by partitioning the interval and
evaluating the function at the midpoints of the subintervals.

Question 6

Use a finite sum to estimate the average value of the function on the given interval by partitioning the interval and
evaluating the function at the midpoints of the subintervals.

Question 7

Question 8

A) 174
B) 165
C) 149
D) 126

Question 9

A) 174
B) 126
C) 149
D) 165

Question 10

Question 11

Use a finite sum to estimate the average value of the function on the given interval by partitioning the interval and
evaluating the function at the midpoints of the subintervals.

Question 12

Use a finite sum to estimate the average value of the function on the given interval by partitioning the interval and
evaluating the function at the midpoints of the subintervals.

Question 13

Question 14

f(x) = 1 - x2 between x = -1 and x = 1 using the "midpoint rule" with two rectangles of equal width.

A) 0.75
B) 0.5
C) 2
D) 1.5

Question 15

Use a finite sum to estimate the average value of the function on the given interval by partitioning the interval and
evaluating the function at the midpoints of the subintervals.

Question 16

A) 86
B) 54
C) 62
D) 69

Question 17

A) 5
B) 4.5
C) 1
D) 2.5

Question 18

Use a finite sum to estimate the average value of the function on the given interval by partitioning the interval and
evaluating the function at the midpoints of the subintervals.

Question 19

A) )75
B) )625
C) )125
D) )3145

Question 20

Use a finite sum to estimate the average value of the function on the given interval by partitioning the interval and
evaluating the function at the midpoints of the subintervals.

Question 21

Write the sum without sigma notation and evaluate it.

Question 22

Write the sum without sigma notation and evaluate it.

Question 23

A swimming pool has a leak. The leak is getting worse. The following table gives the leakage rate every 6 hours. Give the upper estimate for the number of gallons lost.

A) 32.9 gallons
B) 197.4 gallons
C) 257.4 gallons
D) 145.2 gallons

Question 24

Write the sum without sigma notation and evaluate it.

Question 25

Write the sum without sigma notation and evaluate it.

Question 26

Write the sum without sigma notation and evaluate it.

Question 27

Estimate the value of the quantity.
The table gives dye concentrations for a cardiac-output determination. The amount of dye injected was 4.6 mg. Plot the data and connect the data points with a smooth curve. Find the
Area under the curve using rectangles. Use this area to estimate the cardiac output.

A) 285.7 L/min
B) 12.6 L/min
C) 0.1 L/min
D) 6.3 L/min

Question 28

Joe wants to find out how far it is across the lake. His boat has a speedometer but no odometer. The table shows the boats velocity at 10 second intervals. Estimate the distance across the lake
Using right-end point values.

A) 5900 ft
B) 391 ft
C) 3910 ft
D) 4010 ft

Question 29

Write the sum without sigma notation and evaluate it.

Question 30

Estimate the value of the quantity.
The table gives dye concentrations for a cardiac-output determination. The amount of dye injected was 5.0 mg. Plot the data and connect the data points with a smooth curve. Find the
Area under the curve using rectangles. Use this area to estimate the cardiac output.

A) 381.6 L/min
B) 18.9 L/min
C) 9.4 L/min
D) 0.2 L/min

Question 31

Estimate the value of the quantity.
The table shows the velocity of a remote controlled race car moving along a dirt path for 8 seconds. Estimate the distance traveled by the car using 8 subintervals of length 1 with
Right-end point values.

A) 172 in.
B) 182 in.
C) 188 in.
D) 178 in.

Question 32

A hat is dropped from a hot air balloon. The hat falls faster and faster but its acceleration decreases over time due to air resistance. The acceleration is measured every second after the
Drop for 6 seconds. Find an upper estimate for the speed when t = 8 seconds.

A) 65.35 ft/sec
B) 33.98 ft/sec
C) 32.04 ft/sec
D) 192 ft/sec

Question 33

A swimming pool has a leak. The leak is getting worse. The following table gives the leak rate every 6 hours. Suppose it keeps leaking 6.3 gallons every 6 hours. After losing 2700 gallons the leak is fixed.
Approximately how long did the leak last? Use the right endpoints to estimate the first 48
Hours.

A) 54.59 hours
B) 32.48 hours
C) 26.48 hours
D) -87.60 hours

Question 34

Write the sum without sigma notation and evaluate it.

Question 35

The velocity of a projectile fired straight into the air is given every half second. Use right endpoints to estimate the distance the projectile travelled in four seconds.

A) 471.8 m
B) 982.8 m
C) 491.4 m
D) 943.6 m

Question 36

A piece of tissue paper is picked up in gusty wind. The table shows the velocity of the paper at 2 second intervals. Estimate the distance the paper travelled using left-endpoints.

A) 256 ft
B) 233 ft
C) 236 ft
D) 128 ft

Question 37

Write the sum without sigma notation and evaluate it.

Question 38

Estimate the value of the quantity.
The table shows the velocity of a remote controlled race car moving along a dirt path for 8 seconds. Estimate the distance traveled by the car using 8 subintervals of length 1 with
Left-end point values.

A) 328 in.
B) 164 in.
C) 169 in.
D) 154 in.

Question 39

Write the sum without sigma notation and evaluate it.

Question 40

Write the sum without sigma notation and evaluate it.

Question 41

Provide an appropriate response.

Question 42

Express the sum in sigma notation.

Question 43

Find the value of the specified finite sum.

Question 44

Evaluate the sum.

Question 45

Provide an appropriate response.

Question 46

Express the sum in sigma notation.

Question 47

Find the value of the specified finite sum.

Question 48

Evaluate the sum.

Question 49

Evaluate the sum.

Question 50

Find the value of the specified finite sum.

Question 51

Evaluate the sum.

Question 52

Express the sum in sigma notation.

Question 53

Evaluate the sum.

Question 54

Evaluate the sum.

Question 55

Provide an appropriate response.

Question 56

Find the value of the specified finite sum.

Question 57

Express the sum in sigma notation.

Question 58

Express the sum in sigma notation.

Question 59

Provide an appropriate response.

Question 60

Find the value of the specified finite sum.

Question 61

Evaluate the sum.

Question 62

Express the limit as a definite integral.

Question 63

Find the formula and limit as requested.

Question 64

Evaluate the sum.

Question 65

Evaluate the sum.

Question 66

Evaluate the sum.

Question 67

Express the limit as a definite integral.

Question 68

Express the limit as a definite integral.

Question 69

Express the limit as a definite integral.

Question 70

Express the limit as a definite integral.

Question 71

Express the limit as a definite integral.

Question 72

Express the limit as a definite integral.

Question 73

Evaluate the sum.

Question 74

Express the limit as a definite integral.

Question 75

Find the formula and limit as requested.

Question 76

Evaluate the sum.

Question 77

Evaluate the sum.

Question 78

Find the formula and limit as requested.

Question 79

Evaluate the sum.

Question 80

Express the limit as a definite integral.