Deck 6: Antiderivatives and Applications

Question 1

Evaluate .

A)
B)
C)
D)

Answer 1

Question 2

The graph of the derivative F' of a function F is shown. Assuming that F(20) = 10, estimate the maximum value attained by F.

Answer 2

364.167 (answers may vary)

Question 3

Find an antiderivative of such that , for some constant a.

A)
B)
C)
D)

Answer 3

Question 4

Choose the function that would correspond to this graph of F'.

A)
B)
C)
D)

Question 5

Find an antiderivative of such that .

A)
B)
C)
D)

Question 6

Evaluate .

A)
B)
C)
D)

Question 7

Suppose and . Find the value of .

Question 8

Given the graph: Estimate the value of to three decimal places.

Question 9

Suppose and . Estimate the value of to 4 decimal places.

Question 10

Choose the function that would correspond to this graph of F'.

A)
B)
C)
D)

Question 11

What is the antiderivative of ?

A)
B)
C)
D)

Question 12

Evaluate .

A)
B)
C)
D)

Question 13

What is the antiderivative of ?

A)
B)
C)
D)

Question 14

Suppose and . Estimate the value of to 4 decimal places.

Question 15

Find the indefinite integral .

A)
B)
C)
D)

Question 16

This figure shows the rate of change of F. Given that F(0) = 2, sketch the graph of F.

Question 17

Suppose and . Find the value of .

Question 18

Find an antiderivative of such that .

A)
B)
C)
D)

Question 19

Find an antiderivative with and , given that .

A)
B)
C)
D)

Question 20

This figure shows the rate of change of F. Given that F(0) = 2, sketch the graph of F.

Question 21

Evaluate . Round to 2 decimal places.

Question 22

Evaluate .

Question 23

Find a possible antiderivative of , where a and b are constants.

A)
B)
C)
D)

Question 24

Find an antiderivative of .

A)
B)
C)
D)

Question 25

Find the indefinite integral , where k is a constant.

A)
B)
C)
D)

Question 26

Find the indefinite integral , where k is a constant.

A)
B)
C)
D)

Question 27

Evaluate .

A)
B)
C)
D)

Question 28

Find the indefinite integral .

A)
B)
C)
D)

Question 29

Propellant is leaking out from the pressurized fuel tanks of the space shuttle, causing the pressure to decrease at a rate of psi per second at time t in seconds. By how many psi has the pressure dropped during the first 30 seconds? Round to 2 decimal places.

Question 30

Find the average value of on the interval to .

Question 31

Evaluate .

Question 32

Find the antiderivative of , where a and b are constants.

A)
B)
C)
D)

Question 33

Find the indefinite integral .

A)
B)
C)
D)

Question 34

Evaluate .

A)
B)
C)
D)

Question 35

Use the Fundamental Theorem of Calculus to determine the value of b if the area under the graph of between and is 8. Assume .

Question 36

Find an antiderivative F of satisfying .

A)
B)
C)
D)

Question 37

Use a definite integral to find the area under the graph of between and . Round to 2 decimal places.

Question 38

Evaluate . Round to 2 decimal places.

Question 39

Evaluate .

Question 40

Evaluate . Round to 2 decimal places.

Question 41

Supply and demand curves for a product are shown in the following figure. Estimate the consumer surplus, to the nearest thousand dollars.

Question 42

The improper integral converges.

Question 43

The following figure shows the demand and supply curves for a product. Estimate the consumer surplus.

A)$1125
B)$1000
C)$400
D)$875

Question 44

Evaluate .

A)
B)
C)
D)

Question 45

The following figure shows the demand and supply curves for a product. At an artificially imposed price of $12, estimate the consumer surplus.

A)$1125
B)$625
C)$825
D)$1300

Question 46

The improper integral converges for all positive values of p.

Question 47

The improper integral diverges.

Question 48

Fuel pressure in the fuel tanks of the space shuttle is decreasing at a rate of psi per second at time t in seconds. By how many total psi has the pressure decreased during the first minute? Round to 2 decimal places.

Question 49

Evaluate .

A)
B)
C)
D)

Question 50

Find .

A)
B)
C)
D)
E)This improper integral diverges.

Question 51

The following figure shows the demand and supply curves for a product. At an artificially imposed price of $14, what quantity will consumers buy?

A)120
B)150
C)190
D)220

Question 52

If converges, find its value. Otherwise, enter "DNC".

Question 53

The following figure shows the demand and supply curves for a product. Estimate the equilibrium quantity.

A)0
B)140
C)250
D)400

Question 54

At time t hours after taking medication, the rate at which the medication is being eliminated from the body is given by mg/hr. Assuming that all of the medication is eventually eliminated, how many mg was the original dose?

Question 55

Supply and demand curves for a product are shown in the following figure. Estimate the equilibrium quantity.

Question 56

A. Use the Fundamental Theorem to find for a constant .
B. Take the limit of your answer to part (A) as to find .

Question 57

The following figure shows the demand and supply curves for a product. Estimate the total gains from trade.

A)$1400
B)$2000
C)$1275
D)$2125

Question 58

If converges, find its value. Otherwise, enter "DNC".

Question 59

If converges, find its value. Otherwise, enter "DNC".

Question 60

Compute .

A)
B)
C)
D)

Question 61

The supply and demand curves for a product have equations and , respectively, with equilibrium at . Which of the following is a formula for producer surplus?

A)
B)
C)
D)
E)

Question 62

Supply and demand curves for a medical equipment product are given in the graph below. a) Estimate the equilibrium price and quantity.
b) Estimate the producer surplus.
c) Estimate the total gains from trade for this piece of equipment.

Question 63

You are considering buying a salt water chlorinator for your swimming pool. The equipment costs $1300, and you estimate that you will save $250 per year with the saltwater system. Will the chlorinator pay for itself in 6 years (i.e. will the present value of the cost of the chemicals equal or exceed the cost of the chlorinator)? Assume an annual interest rate of 7%, compounded continuously. Answer "yes" or "no".

Question 64

The supply and demand curves for a product have equations and , respectively, with equilibrium at . Which of the following is a formula for total gains from trade?

A)
B)
C)
D)
E)

Question 65

Supply and demand curves for an item of medical equipment are shown in the graph below. In order to compete with a new product by a rival company, the price is temporarily lowered to $20,000. What is the reduction (from equilibrium) in producer surplus that results from this artificially low price?

A)The producer surplus is reduced by $ 48,000.
B)The producer surplus is reduced by $ 59,000
C)The producer surplus is unaffected.
D)The producer surplus is reduced by $ 36,000

Question 66

A consultant expects an income stream of $15,000 per year for the next 8 years.
A. Find the present value of this income stream if the interest rate is 2% per year, compounded continuously.
B. Find the future value of this income stream under the same conditions.

Question 67

The demand curve for a product has equation , and the supply curve has equation for , where q is quantity and p is the price per unit. At an artificially high price of $27, find the quantity consumers are willing to purchase and the quantity producers are willing to supply. Use this information to calculate the producer surplus at this price, to the nearest dollar.

Question 68

The supply and demand curves for a product have equations and , respectively, with equilibrium at . Suppose an artificially high price of is imposed, with the resulting consumer demand of . Which of the following is a formula for the change in total gains from trade caused by the artificial price?

A)
B)
C)
D)

Question 69

Supply and demand curves for a product are given by the equations
Demand: Supply: where p is price in dollars and q is quantity. Find the equilibrium price.

Question 70

Supply and demand curves for a product are shown in the following figure. Suppose an artificially low price of $300 is imposed. Estimate the total gains from trade now, to the nearest 500 dollars.

Question 71

Supply and demand curves for a product are given by the equations
Demand: Supply: where p is price in dollars and q is quantity. Compute the producer surplus. Round to the nearest cent.

Question 72

The supply and demand curves for a product have equations and , respectively, with equilibrium at . Which of the following is a formula for consumer surplus?

A)
B)
C)
D)
E)

Question 73

A. Find the present value of an income stream of $1000 per year for a period of 5 years if the interest rate is 8%. Round to the nearest dollar.
B. Find the future value of this income stream. Round to the nearest dollar.

Question 74

Supply and demand data are given in the following tables. What is the equilibrium price?

Question 75

What is the present value of an income stream of $1000 per year for 10 years with an annual interest rate of 10%, compounded continuously? Round to the nearest dollar.

Question 76

Supply and demand data are given in the following tables. Estimate the consumer surplus.

Question 77

From the time a child is born until he is 18, a father plans to set aside $100 times the child's current age each year. Find the present value of this income stream, given an interest rate of 7% compounded continuously. Round to the nearest dollar.

Question 78

The demand curve for a product has equation , and the supply curve has equation for , where q is quantity and p is the price per unit. Use a calculator to find the equilibrium price and quantity, and use this information to calculate the consumer surplus, to the nearest dollar.

Question 79

Supply and demand data are given in the following tables. Which table shows demand?

A)The first one
B)The second one

Question 80

At what constant, continuous annual rate should you deposit money into an account if you want to have $1,000,000 in 20 years? The account earns 5% interest, compounded continuously. Round to the nearest dollar.