Question 1

Evaluate the integral   .

Accepted Answer

A)    
B)    
C)    
D)    
E)  integral diverges 
A)    
B)    
C)    
D)    
E)  integral diverges

Question 2

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 3

The Lorenz curve for the income distribution in a certain country in 2005 is given by   . Find the Gini coefficient of income for 2005 for this country. Round your answer to four decimal places. ​

Accepted Answer

A)  ​0.3576 
B)  0.4648 
C)  0.5614 
D)  0.2103 
E)  0.2668 
A)  ​0.3576 
B)  0.4648 
C)  0.5614 
D)  0.2103 
E)  0.2668

Question 4

Use an integral formula to evaluate   . ​

Accepted Answer

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

Question 5

The graph in the following figure gives the times that it takes a vehicle to reach speeds from 0 mph to 25 mph, in increments of 5 mph, with a curve connecting them. Count the squares under the curve to estimate this distance. Estimate the distance traveled by the vehicle in 14 seconds, to a speed of 25 mph. (Be careful with time units.)

Accepted Answer

A)  1/16 mile 
B)  4/15 mile 
C)  1/13 mile 
D)  1/9 mile 
E)  1/8 mile 
A)  1/16 mile 
B)  4/15 mile 
C)  1/13 mile 
D)  1/9 mile 
E)  1/8 mile

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

Find the value of the sum   ​

Accepted Answer

A)  8,784 
B)  8,808 
C)  5,675 
D)  8,800 
E)  2,622 
A)  8,784 
B)  8,808 
C)  5,675 
D)  8,800 
E)  2,622

Question 8

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 9

The probability density function for the life span of an electronics part is   where t is the number of months in service. Find the probability that any given part of this type lasts longer than 18 months. Round your answer to three decimal places. ​

Accepted Answer

A)  0.487 
B)  0.513 
C)  0.532 
D)  0.497 
E)  0.468 
A)  0.487 
B)  0.513 
C)  0.532 
D)  0.497 
E)  0.468

Question 10

Use integration by parts to evaluate   ​

Accepted Answer

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

Question 11

Find the value of the given sum and round to four decimal places. ​   ​

Accepted Answer

A)  3.2405 
B)  2.3000 
C)  2.5571 
D)  2.0000 
E)  2.6250 
A)  3.2405 
B)  2.3000 
C)  2.5571 
D)  2.0000 
E)  2.6250

Question 12

Evaluate the definite integral   . ​

Accepted Answer

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

Question 13

Find the area between the curve   and the x-axis from   to   . ​

Accepted Answer

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

Question 14

A 58-year-old couple are considering opening a business of their own. They will either purchase an established Gift and Card Shoppe or open a new Video Rental Palace. The Gift Shoppe has a continuous income stream with an annual rate of flow at time t given by   (dollars per year) and the Video Palace has a continuous income stream with a projected annual rate of flow at time t given by   (dollars per year). The initial investment is the same for both businesses, and money is worth 10% compounded continuously. Find the present value of the Video Palace over the next 8 years (until the couple reach age 66). Round your answer to the nearest dollar. ​

Accepted Answer

A)  $222,961 
B)  $220,268 
C)  $202,618 
D)  $237,342 
E)  $181,863 
A)  $222,961 
B)  $220,268 
C)  $202,618 
D)  $237,342 
E)  $181,863

Question 15

Suppose the marginal cost for x units of a good is   (dollars per unit) and if the fixed cost is $200 find the total cost function of the good? ​

Accepted Answer

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

Question 16

Use an integral formula to evaluate   .

Accepted Answer

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

Question 17

The average life for a particular brand of car battery is given by the following probability density function where t is in years.   ​Find the probability that a battery chosen at random lasts between 2 and 7 years. Round your answer to two decimal places. ​

Accepted Answer

A)  1.72 
B)  0.43 
C)  0.54 
D)  0.34 
E)  0.65 
A)  1.72 
B)  0.43 
C)  0.54 
D)  0.34 
E)  0.65

Question 18

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 19

The production from a particular assembly line is considered a continuous income stream with annual rate of flow given by   (in thousands of dollars per year). Use Simpson's Rule with n = 4 to approximate the total income to 2 decimal places over the first 2 years, given by   . ​

Accepted Answer

A)  $107,619.44 
B)  $247,524.72 
C)  $63,305.55 
D)  $333,620.27 
E)  $150,667.22 
A)  $107,619.44 
B)  $247,524.72 
C)  $63,305.55 
D)  $333,620.27 
E)  $150,667.22

Question 20

Find the area of the shaded region. ​
​

Accepted Answer

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

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.

The Lorenz curve for the income distribution in a certain country in 2005 is given by . Find the Gini coefficient of income for 2005 for this country. Round your answer to four decimal places.

Use an integral formula to evaluate .

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

Find the value of the sum

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).

The probability density function for the life span of an electronics part is where t is the number of months in service. Find the probability that any given part of this type lasts longer than 18 months. Round your answer to three decimal places.

Use integration by parts to evaluate

Find the value of the given sum and round to four decimal places.

Evaluate the definite integral .

Find the area between the curve and the x-axis from to .

Suppose the marginal cost for x units of a good is (dollars per unit) and if the fixed cost is $200 find the total cost function of the good?

Use an integral formula to evaluate .

The average life for a particular brand of car battery is given by the following probability density function where t is in years. Find the probability that a battery chosen at random lasts between 2 and 7 years. Round your answer to two decimal places.

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

The production from a particular assembly line is considered a continuous income stream with annual rate of flow given by (in thousands of dollars per year). Use Simpson's Rule with n = 4 to approximate the total income to 2 decimal places over the first 2 years, given by .

Find the area of the shaded region.

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

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Exam 13: Definite Integrals - Techniques

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. ​

The Lorenz curve for the income distribution in a certain country in 2005 is given by . Find the Gini coefficient of income for 2005 for this country. Round your answer to four decimal places. ​

Use an integral formula to evaluate . ​

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

Find the value of the sum ​

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). ​

The probability density function for the life span of an electronics part is where t is the number of months in service. Find the probability that any given part of this type lasts longer than 18 months. Round your answer to three decimal places. ​

Use integration by parts to evaluate ​

Find the value of the given sum and round to four decimal places. ​ ​

Evaluate the definite integral . ​

Find the area between the curve and the x-axis from to . ​

Suppose the marginal cost for x units of a good is (dollars per unit) and if the fixed cost is $200 find the total cost function of the good? ​

Use an integral formula to evaluate .

The average life for a particular brand of car battery is given by the following probability density function where t is in years. ​Find the probability that a battery chosen at random lasts between 2 and 7 years. Round your answer to two decimal places. ​

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

The production from a particular assembly line is considered a continuous income stream with annual rate of flow given by (in thousands of dollars per year). Use Simpson's Rule with n = 4 to approximate the total income to 2 decimal places over the first 2 years, given by . ​

Find the area of the shaded region. ​ ​

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

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.

The Lorenz curve for the income distribution in a certain country in 2005 is given by . Find the Gini coefficient of income for 2005 for this country. Round your answer to four decimal places.

Use an integral formula to evaluate .

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

Find the value of the sum

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).

The probability density function for the life span of an electronics part is where t is the number of months in service. Find the probability that any given part of this type lasts longer than 18 months. Round your answer to three decimal places.

Use integration by parts to evaluate

Find the value of the given sum and round to four decimal places.

Evaluate the definite integral .

Find the area between the curve and the x-axis from to .

Suppose the marginal cost for x units of a good is (dollars per unit) and if the fixed cost is $200 find the total cost function of the good?

The average life for a particular brand of car battery is given by the following probability density function where t is in years. Find the probability that a battery chosen at random lasts between 2 and 7 years. Round your answer to two decimal places.

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

The production from a particular assembly line is considered a continuous income stream with annual rate of flow given by (in thousands of dollars per year). Use Simpson's Rule with n = 4 to approximate the total income to 2 decimal places over the first 2 years, given by .

Find the area of the shaded region.