Question : Suppose that the accompanying table shows the velocity of acar every second for 8 seconds. Use the trapezoida : 2163452
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Divide the given interval into n subintervals and list the value of Δx and the endpoints a0, a1, ... , an of the subintervals.
1) -5 ≤ x ≤ 2; n = 5
A) Δx = 1.4; a0 = -5, a1 = -3.6, a2 = -2.2, a3 = -0.8, a4 = 0.6, a5 = 2
B) Δx = 1.4; a0 = -5, a1 = -4.3, a2 = -2.2, a3 = -0.8, a4 = 1.3, a5 = 2
C) Δx = 0.4; a0 = -5, a1 = -4.3, a2 = -2.9, a3 = -0.8, a4 = 0.6, a5 = 2
D) Δx = 1.75; a0 = -5, a1 = -3.25, a2 = -1.5, a3 = 0.25, a4 = 2
Divide the interval into n subintervals and list the value of Δx and the midpoints x1, ... , xn of the subintervals.
2) -1 ≤ x ≤ 2; n = 6
A) Δx = 0.5; x1 = -0.5, x2 = 0, x3 = 0.5, x4 = 1, x5 = 1.5, x6 = 2
B) Δx = 0.5; x1 = -0.5, x2 = -0.25, x3 = 0.25, x4 = 0.75, x5 = 1.25, x6 = 2
C) Δx = 0.25; x1 = -0.75, x2 = -0.25, x3 = 0.25, x4 = 0.75, x5 = 1.25, x6 = 1.75
D) Δx = 0.5; x1 = -0.75, x2 = -0.25, x3 = 0.25, x4 = 0.75, x5 = 1.25, x6 = 1.75
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Approximate the integral by the midpoint rule.
3) Approximate 
(1/x)dx; n = 4
Enter just a real number rounded to two decimal places.
4) A homeowner has fences on three sides of her property and astream runs along the fourth side. She makes measurements of the distance to the stream every 10 feet as illustrated. What is the approximate area of her property?
Enter just an integer (no units).
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Approximate the integral by the trapezoidal rule.
5) 
dx; n = 4
Express your answer to four decimal places.
A) 0.6196
B) 1.2392
C) 0.9593
D) 4.9568
6) 
dx; n = 4
Express your answer to five decimal places.
A) 4.81709
B) 2.40854
C) 9.63417
D) 1.50455
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
7) 
dx; n = 4
Enter just a real number rounded to two decimal places.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
8) The following data give the marginal cost for different levels of production at Zipperty-Doo-Dah Inc. Here x represents the number of zippers produced and C'(x) is in dollars per zipper. Approximate the total in going from a production level of 40 zippers to 80 zippers.
A) $85.50
B) $27.20
C) $136.00
D) $272.00
Use n = 4to approximate the value of the integral by the trapezoidal rule.
9) 
A) (141/50)
B) (141/25)
C) (71/25)
D) (141/100)
10) 
A) (3513/560)
B) (3513/280)
C) (1747/560)
D) (2229/280)
Solve the problem. Round your answer, if appropriate.
11) Suppose that the accompanying table shows the velocity of acar every second for 8 seconds. Use the trapezoidal rule to approximate the distance traveled by the car in the 8 seconds.
A) 145.5 feet
B) 221.5 feet
C) 291 feet
D) 162 feet
12) The following table shows the rate of water flow (in gal/min) from astream 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) 9983.3 gallons
B) 9975 gallons
C) 11,350 gallons
D) 9050.0 gallons
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Approximate the integral by the Simpson's rule.
13) 
dx; n = 4
Enter just a real number rounded to two decimal places.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
14) The shaded area in the diagram represents an estimation 
dx using:
A) the midpoint rule with n = 4
B) a Riemann Sum using right endpoints
C) Simpson's rule with n =4
D) a Riemann Sum using left endpoints
E) the trapezoid rule with n = 4
15) Which of the following statements are true?
A) In general, Simpson's rule is more accurate than the midpoint rule.
B) In general, the trapezoid rule is more accurate than the midpoint rule.
C) The error in the trapezoid rule decreases as the number of subintervals increases.
D) In general, the error from the midpoint rule is less than the error from the trapezoid rule.
E) All of these statements are true.
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
16) Approximate 
; n = 4, by (a) the trapezoidal rule, (b) the midpoint rule, and (c) then find the exact value of the integral.
Enter just three integers separated by commas answering (a), (b), (c) in that order but unlabeled.
17) Approximate 
; n = 4, by (a) the trapezoidal rule, (b) the midpoint rule, and (c) then find the exact value of the integral.
Enter just a, b, c where a and b are real numbers to two decimal places (rounded off), and c is an integer, all separated by commas and answering (a), (b), (c) in order but unlabeled.
18) Approximate 
; n = 2, by (a) the trapezoidal rule, (b) the midpoint rule, and (c) then find the exact value of the integral.
Enter just a, b, c where a, b are real numbers rounded to two decimal places, and c is a reduced fraction of form (a/b) all unlabeled and answering the questions in order, separated by commas.
19) Approximate 
; n = 8, by (a) the trapezoidal rule, (b) the midpoint rule, and (c) then find the midpoint rule, and (c) then find the exact value of the integral.
Enter just a, b, c as real numbers all rounded to two decimal places. Do not label, but answer in the above order using commas to separate.
20) Approximate 
dx; n = 2, by (a) the midpoint rule, (b) the trapezoidal rule, and (c) Simpson's rule.
Enter your answers in that order as just unlabeled real numbers rounded to two decimal places, separated by commas.
21) Approximate 
dx; n = 10, by (a) Simpson's rule and (b) the trapezoidal rule.
Enter your answers in that order as just unlabeled real numbers rounded to two decimal places, separated by commas.
22) Approximate 
dx; n = 4, by (a) Simpson's rule and (b) the trapezoidal rule.
Enter your answers in that order as just unlabeled real numbers rounded to two decimal places, separated by a comma.
