Deck 5: Integration

Question 1

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) 149 in.
B) 318 in.
C) 164 in.
D) 159 in.

Answer 1

159 in.

Question 2

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) 142 in.
B) 148 in.
C) 158 in.
D) 152 in.

Answer 2

152 in.

Question 3

Estimate the value of the quantity.

-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) 5000 ft
B) 337 ft
C) 3470 ft
D) 3370 ft

Answer 3

3370 ft

Question 4

Estimate the value of the quantity.

-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) 110 ft
B) 200 ft
C) 197 ft
D) 220 ft

Question 5

Estimate the value of the quantity.

-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) 823.6 m
B) 411.8 m
C) 431.4 m
D) 862.8 m

Question 6

Use a finite approximation to estimate the area under the graph of the given function on the stated interval as instructed.

-f(x) = between x = 0 and x = 4 using a left sum with two rectangles of equal width.

A) 20
B) 38.75
C) 8
D) 40

Question 7

Use a finite approximation to estimate the area under the graph of the given function on the stated interval as instructed.

-f(x) = between x = 0 and x = 4 using a right sum with two rectangles of equal width.

A) 40
B) 8
C) 20
D) 38.75

Question 8

Use a finite approximation to estimate the area under the graph of the given function on the stated interval as instructed.

-f(x) = between x = 0 and x = 3 using the midpoint sum with two rectangles of equal width.

A) 16.875
B) 12.5
C) 3.375
D) 8.4375

Question 9

Use a finite approximation to estimate the area under the graph of the given function on the stated interval as instructed.

-f(x) = between x = 3 and x = 8 using a right sum with two rectangles of equal width.

A) 85/66
B) 45/22
C) 85/176
D) 135/176

Question 10

Use a finite approximation to estimate the area under the graph of the given function on the stated interval as instructed.

-f(x) = between x = 1 and x = 6 using an left sum with two rectangles of equal width.

A) 45/14
B) 15/28
C) 95/14
D) 95/84

Question 11

Use a finite approximation to estimate the area under the graph of the given function on the stated interval as instructed.

-f(x) = between x = 1 and x = 8 using the "midpoint rule" with two rectangles of equal width.

A) 252/275
B) 20888/75625
C) 41776/226875
D) 504/275

Question 12

Use a finite approximation to estimate the area under the graph of the given function on the stated interval as instructed.

-f(x) = between x = 2 and x = 6 using a left sum with four rectangles of equal width.

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

Question 13

Use a finite approximation to estimate the area under the graph of the given function on the stated interval as instructed.

-f(x) = between x = 4 and x = 8 using a right sum with four rectangles of equal width.

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

Question 14

Use a finite approximation to estimate the area under the graph of the given function on the stated interval as instructed.

-f(x) = between x = 4 and x = 8 using the midpoint sum with four rectangles of equal width.

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

Question 15

Use a finite approximation to estimate the area under the graph of the given function on the stated interval as instructed.

-f(x) = 9 - between x = -3 and x = 3 using the midpoint sum with two rectangles of equal width.

A) 13.5
B) 6
C) 40.5
D) 20.25

Question 16

Graph the function f(x) over the given interval. Partition the interval into 4 subintervals of equal length. Then add to your sketch the rectangles associated with the Riemann sum , using the indicated point in the kth subinterval for .

-f(x) = 2x + 2, [0, 2], left-hand endpoint

A)

B)

C)

D)

Question 17

Graph the function f(x) over the given interval. Partition the interval into 4 subintervals of equal length. Then add to your sketch the rectangles associated with the Riemann sum , using the indicated point in the kth subinterval for .

-f(x) = -2x - 4, [0, 2], left-hand endpoint

A)

B)

C)

D)

Question 18

Graph the function f(x) over the given interval. Partition the interval into 4 subintervals of equal length. Then add to your sketch the rectangles associated with the Riemann sum , using the indicated point in the kth subinterval for .

-f(x) = - 2, [0, 8], midpoint

A)

B)

C)

D)

Question 19

Graph the function f(x) over the given interval. Partition the interval into 4 subintervals of equal length. Then add to your sketch the rectangles associated with the Riemann sum , using the indicated point in the kth subinterval for .

-f(x) = - 2, [0, 8], left-hand endpoint

A)

B)

C)

D)

Question 20

Graph the function f(x) over the given interval. Partition the interval into 4 subintervals of equal length. Then add to your sketch the rectangles associated with the Riemann sum , using the indicated point in the kth subinterval for .

-f(x) = - 3, [0, 8], right-hand endpoint

A)

B)

C)

D)

Question 21

Graph the function f(x) over the given interval. Partition the interval into 4 subintervals of equal length. Then add to your sketch the rectangles associated with the Riemann sum , using the indicated point in the kth subinterval for .

-f(x) = -4 , [0, 4], midpoint

A)

B)

C)

D)

Question 22

Graph the function f(x) over the given interval. Partition the interval into 4 subintervals of equal length. Then add to your sketch the rectangles associated with the Riemann sum , using the indicated point in the kth subinterval for .

-f(x) = -4 , [0, 4], left-hand endpoint

A)

B)

C)

D)

Question 23

Graph the function f(x) over the given interval. Partition the interval into 4 subintervals of equal length. Then add to your sketch the rectangles associated with the Riemann sum , using the indicated point in the kth subinterval for .

-f(x) = cos x + 2, [0, 2 $\pi$ ], left-hand endpoint

A)

B)

C)

D)

Question 24

Graph the function f(x) over the given interval. Partition the interval into 4 subintervals of equal length. Then add to your sketch the rectangles associated with the Riemann sum , using the indicated point in the kth subinterval for .

-f(x) = cos x + 4, [0, 2 $\pi$ ], right-hand endpoint

A)

B)

C)

D)

Question 25

Graph the function f(x) over the given interval. Partition the interval into 4 subintervals of equal length. Then add to your sketch the rectangles associated with the Riemann sum , using the indicated point in the kth subinterval for .

-f(x) = cos x + 1, [0, 2 $\pi$ ], midpoint

A)

B)

C)

D)

Question 26

Express the sum in sigma notation.

-1 - 4 + 16 - 64 + 256

A)
B)
C)
D)

Question 27

Express the sum in sigma notation.

-5 + 6 + 7 + 8 + 9 + 10

A) + 5
B) k
C)
D)

Question 28

Express the sum in sigma notation.

- + + +

A)
B)
C)
D)

Question 29

Express the sum in sigma notation.

-2 + 4 + 6 + 8 + 10

A)
B)
C)
D)

Question 30

Express the sum in sigma notation.

-- + - + -

A)
B)
C)
D)

Question 31

Evaluate the sum.

-

A) 10
B) 110
C) 55
D)

Question 32

Evaluate the sum.

-

A) 285
B) 729
C) 2025
D) 900

Question 33

Evaluate the sum.

-

A) 132
B) 84
C) 41
D) 140

Question 34

Evaluate the sum.

-

A) 88
B) 96
C) 84
D) 93

Question 35

Express the limit as a definite integral.

- $\Delta$ ; [ -3, 5]

A) dx
B) dx
C) dx
D) dx

Question 36

Express the limit as a definite integral.

- $\Delta$ ; [ -2, 3]

A)
B)
C)
D)

Question 37

Express the limit as a definite integral.

- $\Delta$ ; [ 1, 14]

A)
B)
C)
D)

Question 38

Graph the integrand and use geometry to evaluate the integral.

-

A)
B) 9
C) 5
D) 15

Question 39

Graph the integrand and use geometry to evaluate the integral.

-

A) 17
B) 68
C) 136
D) 34

Question 40

Graph the integrand and use geometry to evaluate the integral.

-

A)
B) 36
C) 72
D) 24

Question 41

Graph the integrand and use geometry to evaluate the integral.

-

A) 400
B) 20
C) 100
D) 200

Question 42

Graph the integrand and use geometry to evaluate the integral.

-

A) 72
B) 24
C) 144
D) 288

Question 43

Graph the integrand and use geometry to evaluate the integral.

-

A) 12
B) 9
C) 18
D) 3

Question 44

Graph the integrand and use geometry to evaluate the integral.

-

A) 14
B) 42
C) 116
D) 58

Question 45

Graph the integrand and use geometry to evaluate the integral.

-

A) 70
B) 45
C) 35
D) 65

Question 46

Graph the integrand and use geometry to evaluate the integral.

-

A)
B) 18
C) 27
D) 9

Question 47

Graph the integrand and use geometry to evaluate the integral.

-

A) 16 $\pi$
B) 16
C) 8 $\pi$
D) 4 $\pi$

Question 48

Solve the problem.

-Suppose that = -2. Find and .

A) 0; -2
B) 6; -2
C) -2; 2
D) 0; 2

Question 49

Solve the problem.

-Suppose that = -4. Find and .

A) 9; 4
B) -36; 4
C) -36; -
D) 5 ; -4

Question 50

Solve the problem.

-Suppose that = 10. Find and .

A) 0; 10
B) 1; -10
C) -1; -10
D) 1; 10

Question 51

Solve the problem.

-Suppose that f and g are continuous and that and

A) 43
B) 35
C) 14
D) -1

Question 52

Solve the problem.

-Suppose that f and g are continuous and that and

A) 22
B) -30
C) -26
D) -10

Question 53

Solve the problem.

-Suppose that f and g are continuous and that and

A) 11
B) 7
C) -11
D) -7

Question 54

Solve the problem.

-Suppose that h is continuous and that = 4 and Find and

A) 13; -13
B) -13; 13
C) 5; -5
D) -5; 5

Question 55

Solve the problem.

-Suppose that g is continuous and that and Find .

A) 26
B) 2
C) -26
D) -2

Question 56

Solve the problem.

-Suppose that f is continuous and that and Find .

A) 6
B) -12
C) 12
D) -6

Question 57

Solve the problem.

-Suppose that f is continuous and that and Find

A) -6
B) -3
C) 18
D) -18

Question 58

Compute the definite integral as the limit of Riemann sums.

-

A)
B) 8
C) -
D)

Question 59

Compute the definite integral as the limit of Riemann sums.

- dx

A)
B)
C) 0
D) 27

Question 60

Find the area of the shaded region.

-

A) 7.5
B) 10
C) 5
D) 12.5

Question 61

Find the area of the shaded region.

-

A) 25/3
B) 22/3
C) 23/3
D) 26/3

Question 62

Find the area of the shaded region.

-

A) 5/3
B) 23/3
C) 3
D) 5

Question 63

Find the area of the shaded region.

-

A) 22/3
B) 29/3
C) 16/3
D) 38/3

Question 64

Find the area of the shaded region.

-

A) 45
B) 27
C) 18
D) 36

Question 65

Find the area of the shaded region.

-

A) 17/4
B) 9/4
C) 33/4
D) 41/4

Question 66

Find the area of the shaded region.

-

A) 1.25
B) 1.39
C) 1.69
D) 1.50

Question 67

Find the area of the shaded region.

-

A) 5/3
B) 2/3
C) 1/3
D) 4/3

Question 68

Find the area of the shaded region.

-

A) 2
B) $\pi$
C) 2 $\pi$
D) 2 + 2 $\pi$

Question 69

Find the area of the shaded region.

-

A) $\pi$ -2
B) $\pi$ + 2
C) $\pi$
D) 2

Question 70

Evaluate the integral.

- dx

A) 108
B) 18
C) 72
D) 162

Question 71

Evaluate the integral.

- dx

A) 6335
B) 91
C) -1267
D) 1267

Question 72

Evaluate the integral.

-

A) 45
B) 64
C) 255
D)

Question 73

Evaluate the integral.

- dx

A) 37/6
B) 5/6
C)15/2
D) 29/6

Question 74

Evaluate the integral.

-

A) 32
B) 92/5
C) 72/5
D) 77/5

Question 75

Evaluate the integral.

-

A) 0
B) 1
C) -22
D) 22

Question 76

Evaluate the integral.

-

A) 18
B) - 36
C) -18
D) 36

Question 77

Evaluate the integral.

-

A) -6
B) 0
C) -3
D) 3

Question 78

Evaluate the integral.

-

A) -10
B) 10
C) 0
D) 5

Question 79

Evaluate the integral.

-

A) -
B)
C) +
D) -

Question 80

Evaluate the integral.

-

A) 9/2
B) 9
C) 4
D) 8