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Question : When we use Simpson's rule, it is necessary that the number of subintervals be : 2151788

Use your calculator to approximate the integral using the method indicated, with n = 100. Round your answer to four decimal places.

20) dx (trapezoidal rule)

A) 19.0349

B) 19.0855

C) 19.0870

D) 20.0855

21) dx (trapezoidal rule)

A) 9.7873

B) 9.6718

C) 9.8093

D) 9.7516

22) dx (trapezoidal rule)

A) 12.7991

B) 12.8501

C) 12.8227

D) 12.8473

23) dx (trapezoidal rule)

A) 0.6520

B) 0.5982

C) 0.6363

D) 0.5980

24) dx (Simpson's rule)

A) 12.6931

B) 12.6105

C) 12.7213

D) 12.7269

25) dx (Simpson's rule)

A) 14.0661

B) 14.0790

C) 14.1178

D) 14.0598

26) dx (Simpson's rule)

A) 6.3895

B) 6.2916

C) 7.3891

D) 6.3893

27) dx (Simpson's rule)

A) 4.3969

B) 4.4037

C) 4.4646

D) 4.4602

Solve the problem. Round your answer, if appropriate.

28) Suppose that the accompanying table shows the velocity of a car every second for 8 seconds. Use the trapezoidal rule to approximate the distance traveled by the car in the 8 seconds.

A) 189 feet

B) 257.5 feet

C) 339 feet

D) 169.5 feet

29) Suppose that the accompanying table shows the velocity of a car every second for 8 seconds. Use Simpson's rule to approximate the distance traveled by the car in the 8 seconds.

A) 169.50 feet

B) 168.33 feet

C) 126.00 feet

D) 170.33 feet

30) The following table shows the rate of water flow (in gal/min) from a stream into a pond during a 30-minute period after a thunderstorm. Use the trapezoidal rule to estimate the total amount of water flowing into the pond during this period.

A) 7850 gallons

B) 6383.3 gallons

C) 6983.3 gallons

D) 6975 gallons

31) The following table shows the rate of water flow (in gal/min) from a stream into a pond during a 30-minute period after a thunderstorm. Use Simpson's rule to estimate the total amount of water flowing into the pond during this period.

A) 6383.3 gallons

B) 6975 gallons

C) 7975 gallons

D) 6983.3 gallons

32) A surveyor measured the length of a piece of land at 100-ft intervals (x), as shown in the table. Use the trapezoidal rule to estimate the area of the piece of land in square feet.

A) 21,000 ft^{2}

B) 20,500 ft^{2}

C) 24,500 ft^{2}

D) 20,000 ft^{2}

33) A surveyor measured the length of a piece of land at 100-ft intervals (x), as shown in the table. Use Simpson's rule to estimate the area of the piece of land in square feet.

A) 22,500 ft^{2}

B) 23,000 ft^{2}

C) 22,000 ft^{2}

D) 27,000 ft^{2}

34) The growth rate of a certain tree (in feet) is given by

y = (2/t + 1) + e^{-t^2/2} ,

where t is time in years. Estimate the total growth of the tree through the end of the second year by using the trapezoidal rule with n = 2.

A) 2.70 feet

B) 3.51 feet

C) 5.41 feet

D) 1.75 feet

35) The growth rate of a certain tree (in feet) is given by

y = (2/t + 1) + e^{-t^2/2} ,

where t is time in years. Estimate the total growth of the tree through the end of the second year by using Simpson's rule with n = 2.

A) 2.34 feet

B) 5.11 feet

C) 3.68 feet

D) 3.41 feet

Provide the proper response.

36) Why might we want to use numerical integration?

i) The integral cannot be evaluated by any technique.

ii) The antidifferentiation is complicated.

iii) f(x) is not known.

A) Both ii and iii

B) Both i and iii

C) Both i and ii

D) All of the above

37) To apply the trapezoidal rule, how should the sum of rectangles found by using left endpoints and the sum of rectangles found by using right endpoints be combined?

A) |left endpoint sum - right endpoint sum|

B) left endpoint sum + right endpoint sum

C) (|left endpoint sum - right endpoint sum|/2)

D) (left endpoint sum + right endpoint sum/2)

38) When we use Simpson's rule, it is necessary that the number of subintervals be ? .

A) even

B) a multiple of 3

C) odd

D) a multiple of 4

39) Simpson's rule approximates consecutive portions of the curve with portions of ? .

A) rectangles

B) parabolas

C) trapezoids

D) triangles

40) Which of the following expressions is associated with Simpson's rule?

A) (a - b/3n)

B) (b - a/3n)

C) (b - a/n)

D) (b - a/2n)

41) Given that n is the number of subdivisions, the difference between the true value of an integral and the value given by the trapezoidal rule or Simpson's rule depends on which of the following?

i) n

ii) n^{2}

iii) n^{3}

iv) n^{4}

A) Either iii or iv

B) Either i or ii

C) Either ii or iv

D) Only ii

42) Which of the following numerical integration methods generally gives the best approximation for the same number of subintervals?

A) summation of areas of rectangles

B) the trapezoidal rule

C) Simpson's rule

D) No method is generally best.