Question 1

Evaluate the integral   . ​

Accepted Answer

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

Question 2

Find the area of the region enclosed by   and   . ​​

Accepted Answer

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

Question 3

Use an integral formula to evaluate   . ​

Accepted Answer

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

Question 4

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 5

If the demand function for a 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 consumer's surplus. Round your answer to the nearest million dollars. ​​

Accepted Answer

A) ​270 million dollars 
B) ​267 million dollars 
C) ​257 million dollars 
D) ​181 million dollars 
E) ​219 million dollars 
A) ​270 million dollars 
B) ​267 million dollars 
C) ​257 million dollars 
D) ​181 million dollars 
E) ​219 million dollars

Evaluate the integral .

Find the area of the region enclosed by and .

Use an integral formula to evaluate .

If the demand function for a 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 consumer's surplus. Round your answer to the nearest million dollars.

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

Evaluate the integral . ​

Find the area of the region enclosed by and . ​​

Use an integral formula to evaluate . ​

If the demand function for a 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 consumer's surplus. Round your answer to the nearest million dollars. ​​

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

Evaluate the integral .

Find the area of the region enclosed by and .

Use an integral formula to evaluate .

If the demand function for a 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 consumer's surplus. Round your answer to the nearest million dollars.