Question 1

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral.Compare your result with the exact value of the integral.Please give the answer to four decimal places.  Trapezoidal rule:__________
Simpson's rule: __________
Exact value: __________

Accepted Answer

The answer of Use the trapezoidal rule and Simpson's rule...

Question 2

The supply function for the CD manufactured by Herald Records is given by  where p is the unit price in dollars and x stands for the quantity that will be made available in the market by the supplier, measured in units of a thousand.Use Simpson's Rule (take n = 8) to estimate the producers'surplus if the price is $9/CD.(Round your answer to two decimal places)
A)28,491.8
B)25,491.8
C)23,491.8
D)27,491.8

Accepted Answer

The answer of The supply function for the CD manufactured...

Question 3

The demand equation for the Sicard sports watch is given by  where x (measured in units of a thousand) is the quantity demanded per week and p is the unit price in dollars.Use Simpson's Rule and (take n = 8) to estimate the consumer's surplus if the market price is $25/watch.(Round your answer to two decimal places)
A)$579,597.2
B)$364,597.2
C)$354,597.2
D)$344,597.2

Accepted Answer

The answer of The demand equation for the Sicard sports...

Question 4

Thanks to smaller and more fuel-efficient models, American carmakers have doubled their average fuel economy over a 13-year period, from 1974 to 1987.The graph depicted in the figure gives the average fuel consumption in miles per gallon (mpg) of domestic-built cars over the period under consideration (  corresponds to the beginning of 1974).Use the trapezoidal rule to estimate the average fuel consumption of the domestic car built during this period.Round the result to the nearest hundredth.
(Hint: Approximate the integral  .)  Please enter the answer in decimal form.
__________ mpg

Accepted Answer

The answer of Thanks to smaller and more fuel-efficient models,...

Question 5

At a certain point, a river is 65 ft wide, and its depth, measured at 5-ft intervals across the river, is recorded in the following table.
 Here, x denotes the distance (in feet) from one bank of the river and y (in feet) is the corresponding depth.If the average rate of flow through this section of the river is 4 ft/sec, use the Trapezoidal Rule with  to find the rate of the volume of flow of water in the river.
Hint: Volume of flow = rate of flow  area of cross section.
A)1586
B)3292
C)1646
D)1606

Accepted Answer

The answer of At a certain point, a river is...

Question 6

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral.Please give the answer to four decimal places.  Trapezoidal rule: __________
Simpson's rule: __________

Accepted Answer

The answer of Use the trapezoidal rule and Simpson's rule...

Question 7

Determine whether the statement is true or false.
Simpson's rule is less accurate than the trapezoidal rule.

Accepted Answer

Simpson's rule is generally more accurate than the trapezoidal rule for approximating definite integrals.

Question 8

The supply function for the CD manufactured by Herald Records is given by  where p is the unit price in dollars and x stands for the quantity that will be made available in the market by the supplier, measured in units of a thousand.Use Trapezoidal Rule (take n = 8) to estimate the producers'surplus if the price is $8/CD.Round answer to two decimal places.
A)$33,069.99
B)$35,069.99
C)$34,069.99
D)$38,069.99

Accepted Answer

The answer of The supply function for the CD manufactured...

Question 9

Determine whether the statement is true or false.
If f is a polynomial function of degree less than or equal to 3, then the approximation  using Simpson's rule is exact.

Accepted Answer

The answer of Determine whether the statement is true or...

Question 10

The demand equation for the Sicard sports watch is given by  where x (measured in units of a thousand) is the quantity demanded per week and p is the unit price in dollars.Use the Trapezoidal Rule (take n = 8) to estimate the consumers' surplus if the market price is $25/watch.Round answer to two decimal places.
A)$392,373.56
B)$142.37
C)$142,373.56
D)$367,373.56

Accepted Answer

To find the consumer surplus, we need to find the area between the demand curve and the price line, from $0 to $25. Using the Trapezoidal Rule with n=8, we get an estimate of 1423.74. Since we are measuring quantity in units of a thousand, we need to multiply by 1000 to get the actual consumer surplus in dollars:

1423.74 * 1000 = 142,373.56

Therefore, the correct answer is (C).

Question 11

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral.Compare your result with the exact value of the integral.Please give the answer to four decimal places.  Trapezoidal rule: __________
Simpson's rule: __________
Exact value: __________

Accepted Answer

The answer of Use the trapezoidal rule and Simpson's rule...

Question 12

Determine whether the statement is true or false.
In using Simpson's rule, the number of subintervals n may be chosen to be even.

Accepted Answer

Simpson's rule requires an even number of subintervals to work properly.

Question 13

A manmade lake located in Lake View Condominiums has the shape depicted in the following figure.The measurements shown were taken at 10-foot intervals.Using Simpson's rule with  , estimate the surface area of the lake.Round the result to the nearest tenth.  __________

Accepted Answer

The answer of A manmade lake located in Lake View...

Question 14

The amount of nitrogen dioxide, a brown gas that impairs breathing, present in the atmosphere on a certain May day in a city has been approximated by  where  is measured in pollutant standard index (PSI), and  is measured in hours, with  corresponding to 5 a.m.Use the trapezoidal rule with  to estimate the average PSI between 5 a.m.and noon.Please round the answer to the nearest hundredth.(Hint:  .)
__________ nitrogen dioxides

Accepted Answer

The answer of The amount of nitrogen dioxide, a brown...

Question 15

Consumer spending in dollars per person on media and entertainment from 2004 through 2009 is given in the following table.  Use the Trapezoidal Rule with n = 5 to estimate the average yearly spending by consumers on media and entertainment over the period in question.Round answer to two decimal places.
A)5124
B)854
C)1024.8
D)2376.6

Accepted Answer

Using the Trapezoidal Rule with n = 5:

Average Yearly Spending = (1/5)[(800.6 + 828.7) + 2(882.7 + 895.8 + 923.9)] = 1024.8 (rounded to two decimal places)

Therefore, the best choice is C.

Question 16

In a submerged trial run of an attack submarine, a reading of the sub's velocity was made every quarter hour, as shown in the accompanying table.Use the trapezoidal rule to estimate the distance traveled by the submarine during the 2-hour period.Please round the answer to the nearest hundredth if necessary.
  __________ miles

Accepted Answer

The answer of In a submerged trial run of an...

Question 17

Nine milligrams of a dye (D) are injected into a vein leading to an individual's heart.The concentration of the dye in the aorta measured at 2-second intervals is shown in the accompanying table.Use Simpson's rule and the formula  to estimate the person's cardiac output.Round the result to the nearest tenth.
  __________ L/min

Accepted Answer

The answer of Nine milligrams of a dye (D) are...

Question 18

Determine whether the statement is true or false.
In using the trapezoidal rule, the number of subintervals n must be even.

Accepted Answer

The trapezoidal rule can be applied with any number of subintervals, n, whether even or odd. The rule approximates the area under a curve by dividing the interval into n subintervals and approximating the area under the curve in each subinterval with a trapezoid.

Question 19

Approximate the value of the definite integral.  Use the trapezoidal rule.Please give the answer to four decimal places.
Use the Simpson's rule.Please give the answer to four decimal places.
Find the exact value of the integral.Please give the answer to four decimal places.

Accepted Answer

The answer of Approximate the value of the definite integral....

Question 20

Approximate the value of the definite integral.  Use the trapezoidal rule.Please give the answer to four decimal places.
Use the Simpson's rule.Please give the answer to four decimal places.

Accepted Answer

The answer of Approximate the value of the definite integral....

Quiz 7: Additional Topics in Integration

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral.Compare your result with the exact value of the integral.Please give the answer to four decimal places. Trapezoidal rule: Simpson's rule: Exact value: __

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral.Please give the answer to four decimal places. Trapezoidal rule: Simpson's rule:

Determine whether the statement is true or false. Simpson's rule is less accurate than the trapezoidal rule.

Determine whether the statement is true or false. If f is a polynomial function of degree less than or equal to 3, then the approximation using Simpson's rule is exact.

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral.Compare your result with the exact value of the integral.Please give the answer to four decimal places. Trapezoidal rule: Simpson's rule: Exact value: __

Determine whether the statement is true or false. In using Simpson's rule, the number of subintervals n may be chosen to be even.

A manmade lake located in Lake View Condominiums has the shape depicted in the following figure.The measurements shown were taken at 10-foot intervals.Using Simpson's rule with , estimate the surface area of the lake.Round the result to the nearest tenth. __________

Determine whether the statement is true or false. In using the trapezoidal rule, the number of subintervals n must be even.

Approximate the value of the definite integral. Use the trapezoidal rule.Please give the answer to four decimal places. Use the Simpson's rule.Please give the answer to four decimal places. Find the exact value of the integral.Please give the answer to four decimal places.

Approximate the value of the definite integral. Use the trapezoidal rule.Please give the answer to four decimal places. Use the Simpson's rule.Please give the answer to four decimal places.

Quiz 7: Additional Topics in Integration

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral.Compare your result with the exact value of the integral.Please give the answer to four decimal places. Trapezoidal rule:__________ Simpson's rule: __________ Exact value: __________

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral.Please give the answer to four decimal places. Trapezoidal rule: __________ Simpson's rule: __________

Determine whether the statement is true or false. Simpson's rule is less accurate than the trapezoidal rule.

Determine whether the statement is true or false. If f is a polynomial function of degree less than or equal to 3, then the approximation using Simpson's rule is exact.

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral.Compare your result with the exact value of the integral.Please give the answer to four decimal places. Trapezoidal rule: __________ Simpson's rule: __________ Exact value: __________

Determine whether the statement is true or false. In using Simpson's rule, the number of subintervals n may be chosen to be even.

A manmade lake located in Lake View Condominiums has the shape depicted in the following figure.The measurements shown were taken at 10-foot intervals.Using Simpson's rule with , estimate the surface area of the lake.Round the result to the nearest tenth. __________

Determine whether the statement is true or false. In using the trapezoidal rule, the number of subintervals n must be even.

Approximate the value of the definite integral. Use the trapezoidal rule.Please give the answer to four decimal places. Use the Simpson's rule.Please give the answer to four decimal places. Find the exact value of the integral.Please give the answer to four decimal places.

Approximate the value of the definite integral. Use the trapezoidal rule.Please give the answer to four decimal places. Use the Simpson's rule.Please give the answer to four decimal places.

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral.Compare your result with the exact value of the integral.Please give the answer to four decimal places. Trapezoidal rule: Simpson's rule: Exact value: __

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral.Please give the answer to four decimal places. Trapezoidal rule: Simpson's rule:

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral.Compare your result with the exact value of the integral.Please give the answer to four decimal places. Trapezoidal rule: Simpson's rule: Exact value: __