Question 1

Use integration by parts to evaluate   . Note that evaluation may require integration by parts more than once. ​

Accepted Answer

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

Question 2

Approximate the area under the curve defined by the function   over the interval x = 0 to x = 3 using the right-hand endpoints of three subintervals (rectangles). ​

Accepted Answer

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

Question 3

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 4

The demand function for a certain product is given by   , where p is the price and q is the number of units demanded. Find the average price as demand ranges from 35 to 81 units. Round your answer to the nearest penny. ​

Accepted Answer

A)  $834.16 
B)  $420.34 
C)  $1,791.90 
D)  $617.90 
E)  $1,421.16 
A)  $834.16 
B)  $420.34 
C)  $1,791.90 
D)  $617.90 
E)  $1,421.16

Question 5

Suppose that the rate at which a nuclear power plant produces radioactive waste is proportional to the number of years it has been operating, according to   in pounds per year. Suppose also that the waste decays exponentially at a rate of 6% per year. Then the amount of radioactive waste that will accumulate in b years is given by   and this integral evaluates to   . How much waste will accumulate in the long run? Take the limit as   in the integral evaluated. Round your answer to the nearest pound, if it exists. ​

Accepted Answer

A)  Approximately 187,536 pounds of waste will accumulate in the long run. 
B)  Approximately 11,252 pounds of waste will accumulate in the long run. 
C)  Approximately 176,284 pounds of waste will accumulate in the long run. 
D)  0 (No waste will accumulate in the long run.) 
E)    (Waste is produced more rapidly than existing waste decays.) 
A)  Approximately 187,536 pounds of waste will accumulate in the long run. 
B)  Approximately 11,252 pounds of waste will accumulate in the long run. 
C)  Approximately 176,284 pounds of waste will accumulate in the long run. 
D)  0 (No waste will accumulate in the long run.) 
E)    (Waste is produced more rapidly than existing waste decays.)

Question 6

Evaluate the integral   . ​

Accepted Answer

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

Question 7

Suppose that the rate at which a nuclear power plant produces radioactive waste is proportional to the number of years it has been operating, according to   in pounds per year. Suppose also that the waste decays exponentially at a rate of 6% per year. Then the amount of radioactive waste that will accumulate in b years is given by   and this integral evaluates to   . How much waste will accumulate in the long run? Take the limit as   in the integral evaluated. Round your answer to the nearest pound, if it exists. ​

Accepted Answer

A)  Approximately 187,536 pounds of waste will accumulate in the long run. 
B)  Approximately 11,252 pounds of waste will accumulate in the long run. 
C)  Approximately 176,284 pounds of waste will accumulate in the long run. 
D)  0 (No waste will accumulate in the long run.) 
E)    (Waste is produced more rapidly than existing waste decays.) 
A)  Approximately 187,536 pounds of waste will accumulate in the long run. 
B)  Approximately 11,252 pounds of waste will accumulate in the long run. 
C)  Approximately 176,284 pounds of waste will accumulate in the long run. 
D)  0 (No waste will accumulate in the long run.) 
E)    (Waste is produced more rapidly than existing waste decays.)

Question 8

With data for 1990 to 2002, the total receipts for world tourism (in billions of dollars per year) can be modeled by the function   where   represents 1985. Find the predicted total receipts for world tourism for the decade from 2003 to 2013. Round your answer to one decimal place. ​

Accepted Answer

A)  $2,982.0 billion 
B)  $15,798.1 billion 
C)  $5,279.3 billion 
D)  $9,277.9 billion 
E)  $12,704.2 billion 
A)  $2,982.0 billion 
B)  $15,798.1 billion 
C)  $5,279.3 billion 
D)  $9,277.9 billion 
E)  $12,704.2 billion

Question 9

Find the area, if it exists, of the region under the graph of y=f(x) and to the right of x=1. ​   ​

Accepted Answer

A)  49 
B)  50 
C)  8 
D)  7 
E)  does not exist 
A)  49 
B)  50 
C)  8 
D)  7 
E)  does not exist

Question 10

Suppose in a small city the response time t (in minutes) of the fire company is given by the probability density function   . For a fire chosen at random, find the probability that the response time is 10 minutes or less. Round your answer to three decimal places. ​

Accepted Answer

A)  0.242 
B)  0.567 
C)  0.391 
D)  0.758 
E)  0.609 
A)  0.242 
B)  0.567 
C)  0.391 
D)  0.758 
E)  0.609

Question 11

Evaluate the integral   . ​

Accepted Answer

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

Question 12

The following table shows the rate of oil consumption (in thousands of barrels per year) by a certain city. Estimate the total consumption of oil by the city from 1999 -2004 by using 5 equal subdivisions and left-hand endpoints to estimate the area under the graph that corresponds to the table from 1999 to 2004.

Accepted Answer

A)  17.704 thousand barrels 
B)  16.632 thousand barrels 
C)  16.816 thousand barrels 
D)  17.546 thousand barrels 
E)  15.689 thousand barrels 
A)  17.704 thousand barrels 
B)  16.632 thousand barrels 
C)  16.816 thousand barrels 
D)  17.546 thousand barrels 
E)  15.689 thousand barrels

Question 13

Use integration by parts to evaluate the integral   ​

Accepted Answer

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

Question 14

The demand function for a certain product is   and the supply function is   where p is in millions of dollars and x is the number of thousands of units. Find the equilibrium point (x, p) and the consumer's surplus there. Round your answer to the nearest million dollars, where applicable. ​

Accepted Answer

A)  Equilibrium point: (4, 64); Consumer's surplus: 43 million dollars 
B)  Equilibrium point: (10, 64); Consumer's surplus: 123 million dollars 
C)  Equilibrium point: (8, 64); Consumer's surplus: 203 million dollars 
D)  Equilibrium point: (4, 8); Consumer's surplus: 187 million dollars 
E)  Equilibrium point: (10, 8); Consumer's surplus: 107 million dollars 
A)  Equilibrium point: (4, 64); Consumer's surplus: 43 million dollars 
B)  Equilibrium point: (10, 64); Consumer's surplus: 123 million dollars 
C)  Equilibrium point: (8, 64); Consumer's surplus: 203 million dollars 
D)  Equilibrium point: (4, 8); Consumer's surplus: 187 million dollars 
E)  Equilibrium point: (10, 8); Consumer's surplus: 107 million dollars

Question 15

Evaluate the integral   . ​

Accepted Answer

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

Question 16

Use the Trapezoidal Rule to approximate   with n = 6. Round your answer to two decimal places. ​

Accepted Answer

A)  97.49 
B)  28.40 
C)  40.70 
D)  18.22 
E)  48.74 
A)  97.49 
B)  28.40 
C)  40.70 
D)  18.22 
E)  48.74

Question 17

Evaluate the definite integral   . ​

Accepted Answer

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

Question 18

Approximate the area under the curve defined by the function   over the interval x = 0 to x = 3 using the right-hand endpoints of three subintervals (rectangles). ​

Accepted Answer

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

Question 19

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 20

Use an integral formula to evaluate   . ​

Accepted Answer

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

Use integration by parts to evaluate . Note that evaluation may require integration by parts more than once.

Approximate the area under the curve defined by the function over the interval x = 0 to x = 3 using the right-hand endpoints of three subintervals (rectangles).

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.

The demand function for a certain product is given by , where p is the price and q is the number of units demanded. Find the average price as demand ranges from 35 to 81 units. Round your answer to the nearest penny.

Evaluate the integral .

With data for 1990 to 2002, the total receipts for world tourism (in billions of dollars per year) can be modeled by the function where represents 1985. Find the predicted total receipts for world tourism for the decade from 2003 to 2013. Round your answer to one decimal place.

Find the area, if it exists, of the region under the graph of y=f(x) and to the right of x=1.

Suppose in a small city the response time t (in minutes) of the fire company is given by the probability density function . For a fire chosen at random, find the probability that the response time is 10 minutes or less. Round your answer to three decimal places.

Evaluate the integral .

Use integration by parts to evaluate the integral

The demand function for a certain product is and the supply function is where p is in millions of dollars and x is the number of thousands of units. Find the equilibrium point (x, p) and the consumer's surplus there. Round your answer to the nearest million dollars, where applicable.

Evaluate the integral .

Use the Trapezoidal Rule to approximate with n = 6. Round your answer to two decimal places.

Evaluate the definite integral .

Approximate the area under the curve defined by the function over the interval x = 0 to x = 3 using the right-hand endpoints of three subintervals (rectangles).

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

Use an integral formula to evaluate .

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Inequalities and Linear Programming

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Mathematics of Finance

Introduction to Probability

Further Topics in Probability and Data Description

Derivatives

Derivatives

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Indefinite Integrals

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Exam 13: A: Definite Integrals - Techniques

Use integration by parts to evaluate . Note that evaluation may require integration by parts more than once. ​

Approximate the area under the curve defined by the function over the interval x = 0 to x = 3 using the right-hand endpoints of three subintervals (rectangles). ​

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. ​ ​

The demand function for a certain product is given by , where p is the price and q is the number of units demanded. Find the average price as demand ranges from 35 to 81 units. Round your answer to the nearest penny. ​

Evaluate the integral . ​

With data for 1990 to 2002, the total receipts for world tourism (in billions of dollars per year) can be modeled by the function where represents 1985. Find the predicted total receipts for world tourism for the decade from 2003 to 2013. Round your answer to one decimal place. ​

Find the area, if it exists, of the region under the graph of y=f(x) and to the right of x=1. ​ ​

Suppose in a small city the response time t (in minutes) of the fire company is given by the probability density function . For a fire chosen at random, find the probability that the response time is 10 minutes or less. Round your answer to three decimal places. ​

Evaluate the integral . ​

Use integration by parts to evaluate the integral ​

The demand function for a certain product is and the supply function is where p is in millions of dollars and x is the number of thousands of units. Find the equilibrium point (x, p) and the consumer's surplus there. Round your answer to the nearest million dollars, where applicable. ​

Evaluate the integral . ​

Use the Trapezoidal Rule to approximate with n = 6. Round your answer to two decimal places. ​

Evaluate the definite integral . ​

Approximate the area under the curve defined by the function over the interval x = 0 to x = 3 using the right-hand endpoints of three subintervals (rectangles). ​

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

Use an integral formula to evaluate . ​

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

Definite Integrals - Techniques

Functions of Two or More Variables

Algebraic Concepts 2

Algebraic Concepts 3

Algebraic Concepts 4

Algebraic Concepts 5

Filters

Use integration by parts to evaluate . Note that evaluation may require integration by parts more than once.

Approximate the area under the curve defined by the function over the interval x = 0 to x = 3 using the right-hand endpoints of three subintervals (rectangles).

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.

The demand function for a certain product is given by , where p is the price and q is the number of units demanded. Find the average price as demand ranges from 35 to 81 units. Round your answer to the nearest penny.

Evaluate the integral .

With data for 1990 to 2002, the total receipts for world tourism (in billions of dollars per year) can be modeled by the function where represents 1985. Find the predicted total receipts for world tourism for the decade from 2003 to 2013. Round your answer to one decimal place.

Find the area, if it exists, of the region under the graph of y=f(x) and to the right of x=1.

Suppose in a small city the response time t (in minutes) of the fire company is given by the probability density function . For a fire chosen at random, find the probability that the response time is 10 minutes or less. Round your answer to three decimal places.

Evaluate the integral .

Use integration by parts to evaluate the integral

The demand function for a certain product is and the supply function is where p is in millions of dollars and x is the number of thousands of units. Find the equilibrium point (x, p) and the consumer's surplus there. Round your answer to the nearest million dollars, where applicable.

Evaluate the integral .

Use the Trapezoidal Rule to approximate with n = 6. Round your answer to two decimal places.

Evaluate the definite integral .

Approximate the area under the curve defined by the function over the interval x = 0 to x = 3 using the right-hand endpoints of three subintervals (rectangles).

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

Use an integral formula to evaluate .