Question 1

Evaluate the integral   . ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 2

Evaluate the definite integral   . ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 3

Suppose that a printing firm considers the production of its presses as a continuous income stream. If the annual rate of flow at time t is given by   in thousands of dollars per year, and if money is worth 7% compounded continuously, find the present value and future value of the presses over the next 10 years. Round your answer to the nearest dollar. ​

Accepted Answer

A)  Present Value: $212,562; Future Value: $428,047 
B)  Present Value: $181,071; Future Value: $364,632 
C)  Present Value: $119,242; Future Value: $240,124 
D)  Present Value: $193,878; Future Value: $390,422 
E)  Present Value: $127,833; Future Value: $257,424 
A)  Present Value: $212,562; Future Value: $428,047 
B)  Present Value: $181,071; Future Value: $364,632 
C)  Present Value: $119,242; Future Value: $240,124 
D)  Present Value: $193,878; Future Value: $390,422 
E)  Present Value: $127,833; Future Value: $257,424

Question 4

Suppose a land developer is planning to dig a small lake and build a group of homes around it. To estimate the cost of the project, the area of the lake must be calculated from the proposed measurements (in feet) given in the following figure and in the table. Use Simpson's Rule to approximate the area of the lake. Round your answer to two decimal places.   where a = 300, b = 200, c = 400 ​

Accepted Answer

A)  64,000 sq ft 
B)  106,666.67 sq ft 
C)  120,000 sq ft 
D)  58,666.67 sq ft 
E)  51,200 sq ft 
A)  64,000 sq ft 
B)  106,666.67 sq ft 
C)  120,000 sq ft 
D)  58,666.67 sq ft 
E)  51,200 sq ft

Question 5

Suppose the following table gives the supply and demand schedules, with p in dollars and x as the number of units. Use Simpson's Rule to approximate the consumer's surplus at market equilibrium. Note that market equilibrium can be found from the tables. ​

Accepted Answer

A)  $33,846 
B)  $27,060 
C)  $29,927 
D)  $13,420 
E)  $31,493 
A)  $33,846 
B)  $27,060 
C)  $29,927 
D)  $13,420 
E)  $31,493

Question 6

Evaluate the improper integral if it converges, or state that it diverges. ​   ​

Accepted Answer

A)    
B)  ​   
C)    
D)    
E)  diverges 
A)    
B)  ​   
C)    
D)    
E)  diverges

Question 7

Use the function   from x = 0 to x = 1 and n equal subintervals with the function evaluated at the left-hand endpoints of each subinterval. Find a formula for the sum of the areas of the n rectangles (call this S). ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 8

Approximate the area under the curve over the specified interval by using the indicated number of subintervals (or rectangles) and evaluating the function at the left-hand endpoints of the subintervals. Compute the approximate area using up to 4 decimal places as needed. ​   from   to     subintervals.
​

Accepted Answer

A)  11.625 square units 
B)  23.25 square units 
C)  19.25 square units 
D)  46.5 square units 
E)  2 square units 
A)  11.625 square units 
B)  23.25 square units 
C)  19.25 square units 
D)  46.5 square units 
E)  2 square units

Question 9

Find the mean of the probability distribution if the probability density function is   . ​

Accepted Answer

A)  54,000 
B)  2 
C)  60 
D)  30 
E)  90 
A)  54,000 
B)  2 
C)  60 
D)  30 
E)  90

Question 10

If the demand function for wheat is   dollars, where x is the number of hundreds of bushels of wheat, estimate the consumer's surplus at   Round answer to the nearest cent. ​

Accepted Answer

A)  $839.61 
B)  $1297.58 
C)  $1679.22 
D)  $1903.12 
E)  $2854.68 
A)  $839.61 
B)  $1297.58 
C)  $1679.22 
D)  $1903.12 
E)  $2854.68

Question 11

The presence of phosphates in certain waste products dumped into a lake promotes the growth of algae. Rampant growth of algae affects the oxygen supply in the water, so an environmental group wishes to estimate the area of algae growth. Group members measure across the algae growth (see the Figure) and obtain the following data (in feet).  
Use Simpson's Rule to approximate the area of the algae growth and round your answer to the nearest square foot.   ​

Accepted Answer

A)  1,110 sq ft 
B)  1,553 sq ft 
C)  2,641 sq ft 
D)  2,019 sq ft 
E)  3,573 sq ft 
A)  1,110 sq ft 
B)  1,553 sq ft 
C)  2,641 sq ft 
D)  2,019 sq ft 
E)  3,573 sq ft

Question 12

Evaluate   . ​

Accepted Answer

A)    
B)  ​   
C)    
D)    
E)    
A)    
B)  ​   
C)    
D)    
E)

Question 13

When the area under   from   to   is approximated, the formulas for the sum of n rectangles using left-hand endpoints and right-hand endpoints are: ​
Left-hand endpoints:   ​
Right-hand endpoints:   ​
Find   and   .
​

Accepted Answer

A)  ​  
​ 
B)  ​  
​ 
C)  ​  
​ 
D)  ​  
​ 
E)  ​  
​ 
A)  ​  
​ 
B)  ​  
​ 
C)  ​  
​ 
D)  ​  
​ 
E)  ​  
​

Question 14

Use an integral formula to evaluate   . ​

Accepted Answer

A)  ​   
B)    
C)    
D)    
E)    
A)  ​   
B)    
C)    
D)    
E)

Question 15

Suppose that a vending machine company is considering selling some of its machines. Suppose further that the income from these particular machines is a continuous stream with an annual rate of flow at time t given by   Find the present value and future value of the machines over the next 3 years if the money is worth 11% compounded continuously. Round answers to the nearest dollar. ​

Accepted Answer

A)  PV = $1,893
FV = $2,633 
B)  ​PV = $1,893
FV = $2,349 
C)  PV = $1,689
FV = $2,349 
D)  PV = $1,689
FV = $2,633 
E)  PV = $2,364
FV = $2,633 
A)  PV = $1,893
FV = $2,633 
B)  ​PV = $1,893
FV = $2,349 
C)  PV = $1,689
FV = $2,349 
D)  PV = $1,689
FV = $2,633 
E)  PV = $2,364
FV = $2,633

Question 16

Use the table values and apply the Simpson's Rule to approximate   to one decimal place.

Accepted Answer

A)  1.7 
B)  1.6 
C)  1.3 
D)  2.0 
E)  2.3 
A)  1.7 
B)  1.6 
C)  1.3 
D)  2.0 
E)  2.3

Question 17

If the supply function for a commodity is   where p is in millions of dollars and x is the number of thousands of units. What is the producer's surplus when 12 thousand units are sold? Round your answer to the nearest million dollars. ​

Accepted Answer

A)  5,623 million dollars 
B)  3,461 million dollars 
C)  3,468 million dollars 
D)  3,999 million dollars 
E)  3,524 million dollars 
A)  5,623 million dollars 
B)  3,461 million dollars 
C)  3,468 million dollars 
D)  3,999 million dollars 
E)  3,524 million dollars

Question 18

Find the area, if it exists, of the region under the graph of   and to the right of   .

Accepted Answer

A)    
B)    
C)    
D)    
E)  does not exist 
A)    
B)    
C)    
D)    
E)  does not exist

Question 19

Use integration by parts to evaluate the integral   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 20

Use integration by parts to evaluate the integral   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Evaluate the integral .

Evaluate the definite integral .

Suppose the following table gives the supply and demand schedules, with p in dollars and x as the number of units. Use Simpson's Rule to approximate the consumer's surplus at market equilibrium. Note that market equilibrium can be found from the tables.

Evaluate the improper integral if it converges, or state that it diverges.

Use the function from x = 0 to x = 1 and n equal subintervals with the function evaluated at the left-hand endpoints of each subinterval. Find a formula for the sum of the areas of the n rectangles (call this S).

Approximate the area under the curve over the specified interval by using the indicated number of subintervals (or rectangles) and evaluating the function at the left-hand endpoints of the subintervals. Compute the approximate area using up to 4 decimal places as needed. from to subintervals.

Find the mean of the probability distribution if the probability density function is .

If the demand function for wheat is dollars, where x is the number of hundreds of bushels of wheat, estimate the consumer's surplus at Round answer to the nearest cent.

Evaluate .

When the area under from to is approximated, the formulas for the sum of n rectangles using left-hand endpoints and right-hand endpoints are: Left-hand endpoints: Right-hand endpoints: Find and .

Use an integral formula to evaluate .

Use the table values and apply the Simpson's Rule to approximate to one decimal place.

If the supply function for a commodity is where p is in millions of dollars and x is the number of thousands of units. What is the producer's surplus when 12 thousand units are sold? Round your answer to the nearest million dollars.

Find the area, if it exists, of the region under the graph of and to the right of .

Use integration by parts to evaluate the integral

Use integration by parts to evaluate the integral

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Derivatives

Derivatives Continued

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A: Definite Integrals - Techniques

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Exam 13: Definite Integrals - Techniques

Evaluate the integral . ​

Evaluate the definite integral . ​

Suppose the following table gives the supply and demand schedules, with p in dollars and x as the number of units. Use Simpson's Rule to approximate the consumer's surplus at market equilibrium. Note that market equilibrium can be found from the tables. ​

Evaluate the improper integral if it converges, or state that it diverges. ​ ​

Use the function from x = 0 to x = 1 and n equal subintervals with the function evaluated at the left-hand endpoints of each subinterval. Find a formula for the sum of the areas of the n rectangles (call this S). ​

Find the mean of the probability distribution if the probability density function is . ​

If the demand function for wheat is dollars, where x is the number of hundreds of bushels of wheat, estimate the consumer's surplus at Round answer to the nearest cent. ​

Evaluate . ​

When the area under from to is approximated, the formulas for the sum of n rectangles using left-hand endpoints and right-hand endpoints are: ​ Left-hand endpoints: ​ Right-hand endpoints: ​ Find and . ​

Use an integral formula to evaluate . ​

Use the table values and apply the Simpson's Rule to approximate to one decimal place.

If the supply function for a commodity is where p is in millions of dollars and x is the number of thousands of units. What is the producer's surplus when 12 thousand units are sold? Round your answer to the nearest million dollars. ​

Find the area, if it exists, of the region under the graph of and to the right of .

Use integration by parts to evaluate the integral ​

Use integration by parts to evaluate the integral ​

Linear Equations and Functions

Quadratic and Other Special Functions

Matrices

Inequalities and Linear Programming

Exponential and Logarithmic Functions

Mathematics of Finance

Introduction to Probability

Further Topics in Probability and Data Description

Derivatives

Derivatives

Derivatives Continued

Indefinite Integrals

A: Definite Integrals - Techniques

Functions of Two or More Variables

Algebraic Concepts 2

Algebraic Concepts 3

Algebraic Concepts 4

Algebraic Concepts 5

Filters

Evaluate the integral .

Evaluate the definite integral .

Suppose the following table gives the supply and demand schedules, with p in dollars and x as the number of units. Use Simpson's Rule to approximate the consumer's surplus at market equilibrium. Note that market equilibrium can be found from the tables.

Evaluate the improper integral if it converges, or state that it diverges.

Use the function from x = 0 to x = 1 and n equal subintervals with the function evaluated at the left-hand endpoints of each subinterval. Find a formula for the sum of the areas of the n rectangles (call this S).

Find the mean of the probability distribution if the probability density function is .

If the demand function for wheat is dollars, where x is the number of hundreds of bushels of wheat, estimate the consumer's surplus at Round answer to the nearest cent.

Evaluate .

When the area under from to is approximated, the formulas for the sum of n rectangles using left-hand endpoints and right-hand endpoints are: Left-hand endpoints: Right-hand endpoints: Find and .

Use an integral formula to evaluate .

If the supply function for a commodity is where p is in millions of dollars and x is the number of thousands of units. What is the producer's surplus when 12 thousand units are sold? Round your answer to the nearest million dollars.

Use integration by parts to evaluate the integral

Use integration by parts to evaluate the integral