Question 1

Equations are given whose graphs enclose a region. Find the area of the region. ​   ​

Accepted Answer

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

Question 2

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 3

Use an integral formula to evaluate   . ​

Accepted Answer

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

Question 4

Evaluate the given integral with the Fundamental Theorem of Calculus   . ​

Accepted Answer

A) -26 
B) -25 
C) -28 
D) -35 
E) -31 
A) -26 
B) -25 
C) -28 
D) -35 
E) -31

Question 5

Find the area of the shaded region for the graph given below.

Accepted Answer

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

Question 6

Evaluate the integral   . ​

Accepted Answer

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

Question 7

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, 70); Consumer's surplus: 43 million dollars 
B) Equilibrium point: (6, 70); Consumer's surplus: 129 million dollars 
C) Equilibrium point: (30, 70); Consumer's surplus: 215 million dollars 
D) Equilibrium point: (4, 30); Consumer's surplus: 199 million dollars 
E) Equilibrium point: (6, 30); Consumer's surplus: 113 million dollars 
A) Equilibrium point: (4, 70); Consumer's surplus: 43 million dollars 
B) Equilibrium point: (6, 70); Consumer's surplus: 129 million dollars 
C) Equilibrium point: (30, 70); Consumer's surplus: 215 million dollars 
D) Equilibrium point: (4, 30); Consumer's surplus: 199 million dollars 
E) Equilibrium point: (6, 30); Consumer's surplus: 113 million dollars

Question 8

Suppose 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. The group measures the length across the algae growth (see the figure) and obtains the following data (in feet).   ​ Use 8 rectangles with bases of 10 feet and lengths measured at the left-hand endpoints to approximate the area of the algae growth.   ​
​

Accepted Answer

A) 1,730 sq ft 
B) 1,704 sq ft 
C) 2,076 sq ft 
D) 2,520 sq ft 
E) 2,556 sq ft 
A) 1,730 sq ft 
B) 1,704 sq ft 
C) 2,076 sq ft 
D) 2,520 sq ft 
E) 2,556 sq ft

Question 9

Use an integral formula to evaluate   . ​

Accepted Answer

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

Question 10

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 11

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 12

If the supply function for x units of a commodity is   dollars, what is the producer's surplus at   ? Round your answer to the nearest dollar. ​

Accepted Answer

A) $8,229 
B) $1,969 
C) $3,741 
D) $1,559 
E) $2,730 
A) $8,229 
B) $1,969 
C) $3,741 
D) $1,559 
E) $2,730

Question 13

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 14

If the marginal cost function for x units of a product is   dollars per unit, and if the fixed cost is $100, find the total cost function. ​

Accepted Answer

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

Question 15

A transmission repair firm that wants to offer a lifetime warranty on its repairs has determined that the probability density function for transmission failure after repair is   , where t is the number of months after repair. What is the probability that a transmission chosen at random will last more than 2 months? Round to 3 decimal places. ​

Accepted Answer

A) 0.348 
B) 0.248 
C) 0.497 
D) 0.546 
E) 0.447 
A) 0.348 
B) 0.248 
C) 0.497 
D) 0.546 
E) 0.447

Question 16

Use integration by parts to evaluate   . ​

Accepted Answer

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

Question 17

Suppose that when a new oil well is opened, its production is viewed as a continuous income stream with monthly rate of flow   where t is time in months and f is in thousands of dollars per month. Find the total income over the next 40 years (480 months). Round your answer to one decimal place. ​

Accepted Answer

A) 41,776.7 thousand dollars 
B) 99,623.7 thousand dollars 
C) 42,023.7 thousand dollars 
D) 61,203.7 thousand dollars 
E) 118,823.7 thousand dollars 
A) 41,776.7 thousand dollars 
B) 99,623.7 thousand dollars 
C) 42,023.7 thousand dollars 
D) 61,203.7 thousand dollars 
E) 118,823.7 thousand dollars

Question 18

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 19

Suppose the rate of production of a new line of products is given by   where x is the number of items produced and t is the number of weeks the products have been in production. How many units were produced in the first 6 weeks? Round your answer to the nearest unit produced. ​

Accepted Answer

A) 1,300 units 
B) 2,300 units 
C) 2,600 units 
D) 1,000 units 
E) 2,000 units 
A) 1,300 units 
B) 2,300 units 
C) 2,600 units 
D) 1,000 units 
E) 2,000 units

Question 20

True or false. For the function   gives the area between the graph of   and the x-axis from   . ​

Accepted Answer

A) True 
B) False 
A) True 
B) False

Equations are given whose graphs enclose a region. Find the area of the region.

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

Use an integral formula to evaluate .

Evaluate the given integral with the Fundamental Theorem of Calculus .

Find the area of the shaded region for the graph given below.

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.

Use an integral formula to evaluate .

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

If the supply function for x units of a commodity is dollars, what is the producer's surplus at ? Round your answer to the nearest dollar.

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.

If the marginal cost function for x units of a product is dollars per unit, and if the fixed cost is $100, find the total cost function.

Use integration by parts to evaluate .

Suppose that when a new oil well is opened, its production is viewed as a continuous income stream with monthly rate of flow where t is time in months and f is in thousands of dollars per month. Find the total income over the next 40 years (480 months). Round your answer to one decimal place.

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 .

Suppose the rate of production of a new line of products is given by where x is the number of items produced and t is the number of weeks the products have been in production. How many units were produced in the first 6 weeks? Round your answer to the nearest unit produced.

True or false. For the function gives the area between the graph of and the x-axis from .

Algebraic Concepts

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; Data Description

Derivatives

Applications of Derivatives

Derivatives Continued

Indefinite Integrals

Functions of Two or More Variables

Filters

Exam 14: Definite Integrals: Techniques of Integration

Equations are given whose graphs enclose a region. Find the area of the region. ​ ​

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

Use an integral formula to evaluate . ​

Evaluate the given integral with the Fundamental Theorem of Calculus . ​

Find the area of the shaded region for the graph given below.

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. ​

Use an integral formula to evaluate . ​

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

If the supply function for x units of a commodity is dollars, what is the producer's surplus at ? Round your answer to the nearest dollar. ​

If the marginal cost function for x units of a product is dollars per unit, and if the fixed cost is $100, find the total cost function. ​

Use integration by parts to evaluate . ​

Suppose that when a new oil well is opened, its production is viewed as a continuous income stream with monthly rate of flow where t is time in months and f is in thousands of dollars per month. Find the total income over the next 40 years (480 months). Round your answer to one decimal place. ​

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 . ​

Suppose the rate of production of a new line of products is given by where x is the number of items produced and t is the number of weeks the products have been in production. How many units were produced in the first 6 weeks? Round your answer to the nearest unit produced. ​

True or false. For the function gives the area between the graph of and the x-axis from . ​

Algebraic Concepts

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; Data Description

Derivatives

Applications of Derivatives

Derivatives Continued

Indefinite Integrals

Functions of Two or More Variables

Filters

Equations are given whose graphs enclose a region. Find the area of the region.

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

Use an integral formula to evaluate .

Evaluate the given integral with the Fundamental Theorem of Calculus .

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.

Use an integral formula to evaluate .

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

If the supply function for x units of a commodity is dollars, what is the producer's surplus at ? Round your answer to the nearest dollar.

If the marginal cost function for x units of a product is dollars per unit, and if the fixed cost is $100, find the total cost function.

Use integration by parts to evaluate .

Suppose that when a new oil well is opened, its production is viewed as a continuous income stream with monthly rate of flow where t is time in months and f is in thousands of dollars per month. Find the total income over the next 40 years (480 months). Round your answer to one decimal place.

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 .

Suppose the rate of production of a new line of products is given by where x is the number of items produced and t is the number of weeks the products have been in production. How many units were produced in the first 6 weeks? Round your answer to the nearest unit produced.

True or false. For the function gives the area between the graph of and the x-axis from .