Question 1

Evaluate the integral   . ​
​

Accepted Answer

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

Question 2

Evaluate   . ​

Accepted Answer

A)  8 
B)  2 
C)  6 
D)  3 
E)  0 
A)  8 
B)  2 
C)  6 
D)  3 
E)  0

Question 3

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 4

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 5

Evaluate the integral   by integration. Round your answer to two decimal places. ​

Accepted Answer

A)  4.00 
B)  9.79 
C)  0.71 
D)  7.34 
E)  3.77 
A)  4.00 
B)  9.79 
C)  0.71 
D)  7.34 
E)  3.77

Question 6

Suppose spending for a wireless communications services (in billions of dollars per year) can be modeled by the function   where   represents 1995. Use   equal subdivisions with right-hand endpoints to approximate the area under the graph of S(t) between   and   . Round your answer to one decimal place. ​

Accepted Answer

A)  1,079.1 billion dollars 
B)  506.5 billion dollars 
C)  575.3 billion dollars 
D)  440.9 billion dollars 
E)  539.5 billion dollars 
A)  1,079.1 billion dollars 
B)  506.5 billion dollars 
C)  575.3 billion dollars 
D)  440.9 billion dollars 
E)  539.5 billion dollars

Question 7

Evaluate the integral   .

Accepted Answer

A)  0 
B)    
C)    
D)    
E)  integral diverges 
A)  0 
B)    
C)    
D)    
E)  integral diverges

Question 8

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

Accepted Answer

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

Question 9

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 10

Determine the most appropriate method or integral formula for evaluating the given integral. Next, evaluate the integral. ​
I. Integration by parts II.  
III.  
IV.

Accepted Answer

A)  I. Integration by parts;   
B)    
C)    
D)  ​   
E)  not integrable by any of the techniques we have studied 
A)  I. Integration by parts;   
B)    
C)    
D)  ​   
E)  not integrable by any of the techniques we have studied

Evaluate the integral .

Evaluate .

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

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

Evaluate the integral by integration. Round your answer to two decimal places.

Suppose spending for a wireless communications services (in billions of dollars per year) can be modeled by the function where represents 1995. Use equal subdivisions with right-hand endpoints to approximate the area under the graph of S(t) between and . Round your answer to one decimal place.

Evaluate the integral .

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

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

Determine the most appropriate method or integral formula for evaluating the given integral. Next, evaluate the integral. I. Integration by parts II. III. IV.

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

Exam 13: A: Definite Integrals - Techniques

Evaluate the integral . ​ ​

Evaluate . ​

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

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

Evaluate the integral by integration. Round your answer to two decimal places. ​

Suppose spending for a wireless communications services (in billions of dollars per year) can be modeled by the function where represents 1995. Use equal subdivisions with right-hand endpoints to approximate the area under the graph of S(t) between and . Round your answer to one decimal place. ​

Evaluate the integral .

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

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

Determine the most appropriate method or integral formula for evaluating the given integral. Next, evaluate the integral. ​ I. Integration by parts II. III. IV.

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

Evaluate the integral .

Evaluate .

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

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

Evaluate the integral by integration. Round your answer to two decimal places.

Suppose spending for a wireless communications services (in billions of dollars per year) can be modeled by the function where represents 1995. Use equal subdivisions with right-hand endpoints to approximate the area under the graph of S(t) between and . Round your answer to one decimal place.

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

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

Determine the most appropriate method or integral formula for evaluating the given integral. Next, evaluate the integral. I. Integration by parts II. III. IV.