Deck 7: Principle of Integral Evaluation

Question 1

Answer true or false. diverges.

Answer 1

False

Question 2

Evaluate .

Answer 2

= = 7

Question 3

Evaluate .

Answer 3

= + = = = = = = = = = + =

Question 4

Answer true or false. is an improper integral.

Question 5

Evaluate .

Question 6

Evaluate .

Question 7

Evaluate .

Question 8

Evaluate .

Question 9

Answer true or false. diverges.

Question 10

Answer true or false. = = -1

Question 11

Answer true or false. diverges.

Question 12

Evaluate .

Question 13

Evaluate

Question 14

Answer true or false. is an improper integral.

Question 15

Answer true or false. diverges.

Question 16

Answer true or false. diverges.

Question 17

Evaluate .

Question 18

Answer true or false. diverges.

Question 19

Evaluate .

Question 20

Evaluate .

Question 21

Use n = 10 to approximate the integral by the midpoint rule.

A) 0.956848
B) 0.952261
C) 0.478424
D) 0.959043
E) 0.377541

Question 22

Evaluate .

Question 23

Evaluate .

Question 24

Evaluate .

Question 25

Evaluate .

Question 26

Evaluate .

Question 27

Evaluate .

Question 28

Evaluate .

Question 29

Evaluate .

Question 30

Evaluate .

Question 31

Evaluate .

Question 32

Evaluate .

Question 33

Evaluate .

Question 34

Evaluate .

Question 35

Evaluate .

Question 36

Use the trapezoid rule with n = 10 to approximate the integral.

A) 2.18713
B) 7.94608
C) 4.37427
D) 3.97304
E) 4.24365

Question 37

Evaluate .

Question 38

Use n = 10 to approximate the integral by the midpoint rule.

A) 100.554
B) 121.654
C) 55.349
D) 110.698
E) 0.200

Question 39

Use n = 10 to approximate the integral by the midpoint rule.

A) 0.121
B) 0.221
C) 0.082
D) 0.165
E) 0.200

Question 40

Use n = 10 to approximate the integral by the midpoint rule.

A) 24.571070
B) 30.972522
C) 38.600681
D) 15.486261
E) 0

Question 41

Use Simpson's Rule with n = 10 to approximate the integral.

Question 42

Use Simpson's Rule with n = 10 to approximate the integral.

Question 43

Use the trapezoid rule with n = 10 to approximate the integral.

A) 12.670000
B) 3.492500
C) 6.335000
D) 6.322375
E) 6.122375

Question 44

Use Simpson's Rule with n = 10 to approximate the integral.

Question 45

Use the trapezoid rule with n = 10 to approximate the integral.

Question 46

Use n = 10 to approximate by the trapezoid rule.

A) 2,666.000000
B) 979.000000
C) 0.000000
D) 1,316.093750
E) 1,003.593750

Question 47

Use Simpson's Rule with n = 10 to approximate the integral.

A) 50.008405
B) 100.016811
C) 22.254692
D) 12.382574
E) 33.338937

Question 48

Use n = 10 to approximate by the midpoint rule.

A) -0.199999
B) 0.199999
C) 0.003
D) 0.01088
E) 6.4

Question 49

Use the trapezoid rule with n = 10 to approximate the integral.

A) 0.135540
B) 0.113379
C) 1.904947
D) 0.067770
E) 0.521595

Question 50

Use Simpson's Rule with n = 10 to approximate the integral.

A) 5.625000
B) 11.250000
C) 3.750000
D) 2.505000
E) 3.516667

Question 51

Use n = 10 to approximate the integral by the midpoint rule.

Question 52

Use n = 10 to approximate by the midpoint rule.

Question 53

Use n = 10 to approximate the integral by the midpoint rule.

Question 54

Use n = 10 to approximate the integral by the midpoint rule.

Question 55

Use the trapezoid rule with n = 10 to approximate the integral.

Question 56

Use the trapezoid rule with n = 10 to approximate the integral.

A) 0.473409
B) 0.397599
C) 0.795199
D) 0.236705
E) 0.125977

Question 57

Use the trapezoid rule with n = 10 to approximate the integral.

Question 58

Use the trapezoid rule with n = 10 to approximate the integral.

Question 59

Use n = 10 to approximate the integral by the midpoint rule.

Question 60

Use Simpson's Rule with n = 10 to approximate the integral.

A) 0.798
B) 0.796
C) 0.794
D) 0.792
E) 0.841

Question 61

Use n = 10 subdivisions to approximate the value of the integral by the trapezoidal approximation.

Question 62

Use n = 10 subdivisions to approximate the value of by the midpoint approximation. Find the exact value of the integral and approximate the magnitude of the error. Express your answer to at least four decimal places.

Question 63

Use n = 10 subdivisions to approximate the value of by Simpson's rule. Find the exact value of the integral and approximate the magnitude of the error. Express your answers to at least four decimal places.

Question 64

Use n = 10 subdivisions to approximate the value of the integral by Simpson's rule.

Question 65

Use inequality (11) to find an upper bound on the magnitude of the error for the approximate value of found by the trapezoidal approximation using 10 subintervals.

Question 66

Use n = 10 subdivisions to approximate the value of the integral by the midpoint approximation.

Question 67

Use n = 10 subdivisions to approximate the value of by Simpson's rule. Find the exact value of the integral and approximate the magnitude of the error. Express your answers to at least four decimal places.

Question 68

Use inequality (12) to find an upper bound on the magnitude of the error for the approximate value of found by Simpson's rule using 2n = 10.

Question 69

Use n = 10 subdivisions to approximate the value of the integral by Simpson's rule.

Question 70

Answer true of false. =

Question 71

Use n = 10 subdivisions to approximate the value of the integral by the midpoint approximation.

Question 72

Answer true or false. = .

Question 73

Answer true or false. For a good choice for u is 3 - 2x².

Question 74

Use n = 10 subdivisions to find the exact value of by the trapezoidal approximation. Find the exact value of the integral and approximate the magnitude of the error. Express your answer to at least four decimal places.

Question 75

Use inequality (10) to find an upper bound on the magnitude of the error for the approximate value of found by the midpoint approximation using 10 subintervals.

Question 76

Use n = 10 subdivisions to approximate the value of by Simpson's rule. Find the exact value of the integral and approximate the magnitude of the error. Express your answers to at least four decimal places.

Question 77

Use n = 10 to approximate by the trapezoid rule.

Question 78

Use n = 10 subdivisions to approximate the value of the integral by the trapezoidal approximation.

Question 79

Use n = 10 subdivisions to approximate the value of by the midpoint approximation. Find the exact value of the integral and approximate the magnitude of the error. Express your answers to at least four decimal places.

Question 80

Use inequality (12) to find an upper bound on the magnitude of the error for the approximate value of found by Simpson's using 2n = 10.