Question 1

Use the Log Rule to find the indefinite integral for   ​

Accepted Answer

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

Question 2

Set up the definite integral that gives the area of the region bounded by the graphs. ​     ​   ​

Accepted Answer

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

Question 3

Evaluate the integral   ​

Accepted Answer

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

Question 4

A ball is thrown vertically upwards from a height of 6 ft with an initial velocity of 40 ft per second. ​
How high will the ball go?
​

Accepted Answer

A)  29.03 ft 
B)  29.34 ft 
C)  30.89 ft 
D)  25.02 ft 
E)  32.12 ft 
A)  29.03 ft 
B)  29.34 ft 
C)  30.89 ft 
D)  25.02 ft 
E)  32.12 ft

Question 5

Evaluate the integral   ​

Accepted Answer

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

Question 6

Use algebra to rewrite the integrand; then integrate and simplify. ​   ​

Accepted Answer

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

Question 7

The revenue from a manufacturing process (in millions of dollars per year)is projected to follow the model   for 10 years.Over the same period of time,the cost (in millions of dollars per year)is projected to follow the model   ,where t is the time (in years).Approximate the profit over the 10-year period,beginning with t = 0.Round your answer to two decimal places. ​

Accepted Answer

A)  $3,236.83 million 
B)  $3,293.50 million 
C)  $3,203.50 million 
D)  $3,235.67 million 
E)  $3,295.67 million 
A)  $3,236.83 million 
B)  $3,293.50 million 
C)  $3,203.50 million 
D)  $3,235.67 million 
E)  $3,295.67 million

Question 8

Evaluate the integral   ​

Accepted Answer

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

Question 9

Find the indefinite integral. ​   ​

Accepted Answer

A)    
B)    
C)    
D)  integral does not exist 
E)  none of the above 
A)    
B)    
C)    
D)  integral does not exist 
E)  none of the above

Question 10

Find the supply function   that satisfies   and the initial condition   when   ​

Accepted Answer

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

Question 11

Evaluate the definite integral of the algebraic function. ​   ​
Use a graphing utility to verify your results.
​

Accepted Answer

A)  825 
B)  33 
C)  -33 
D)  27 
E)  -825 
A)  825 
B)  33 
C)  -33 
D)  27 
E)  -825

Question 12

The integrand of the following definite integral is a difference of two functions. ​   ​
Sketch the graph of the two functions and shade the region whose area is represented by the integral.
​

Accepted Answer

A)  ​  
1)  
2)   
B)  ​  
1)  
2)   
C)  ​  
1)  
2)   
D)  ​  
1)  
2)   
E)  ​  
1)  
2)   
A)  ​  
1)  
2)   
B)  ​  
1)  
2)   
C)  ​  
1)  
2)   
D)  ​  
1)  
2)   
E)  ​  
1)  
2)

Question 13

Use the Midpoint Rule with n = 4 to approximate the area of the following region.Round your answer to 3 decimal places. ​   ​   ​

Accepted Answer

A)  1.156 
B)  1.324 
C)  1.575 
D)  1.275 
E)  1.876 
A)  1.156 
B)  1.324 
C)  1.575 
D)  1.275 
E)  1.876

Question 14

Use formal substitution to find the indefinite integral   ​

Accepted Answer

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

Question 15

Use the Midpoint Rule n = 4 to approximate the area of the following region. ​   ​   ​

Accepted Answer

A)  2.748 
B)  1.788 
C)  1.875 
D)  1.748 
E)  3.951 
A)  2.748 
B)  1.788 
C)  1.875 
D)  1.748 
E)  3.951

Question 16

Find the area of the region bounded by the graphs. ​   ​
1)   2)   ​

Accepted Answer

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

Question 17

Use the values   and   to evaluate the definite integral   ​

Accepted Answer

A)  79 
B)  -83 
C)  0 
D)  18 
E)  -74 
A)  79 
B)  -83 
C)  0 
D)  18 
E)  -74

Question 18

Use the Midpoint Rule with   to approximate the area of the region bounded by the graph of the function and the x-axis over the interval.Sketch the region. ​   ​

Accepted Answer

A)  The approximate area is: ≈ 33.57   
B)  The approximate area is: ≈ 39.05   
C)  The approximate area is: ≈ 34.25   
D)  The approximate area is: ≈ 26.37   
E)  The approximate area is: ≈ 30.14   
A)  The approximate area is: ≈ 33.57   
B)  The approximate area is: ≈ 39.05   
C)  The approximate area is: ≈ 34.25   
D)  The approximate area is: ≈ 26.37   
E)  The approximate area is: ≈ 30.14

Question 19

Find the indefinite integral   and check your result by differentiation. ​

Accepted Answer

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

Question 20

Find the area of the region bounded by the graphs. ​   1)   2)   ​

Accepted Answer

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

Use the Log Rule to find the indefinite integral for

Set up the definite integral that gives the area of the region bounded by the graphs.

Evaluate the integral

A ball is thrown vertically upwards from a height of 6 ft with an initial velocity of 40 ft per second. How high will the ball go?

Evaluate the integral

Use algebra to rewrite the integrand; then integrate and simplify.

Evaluate the integral

Find the indefinite integral.

Find the supply function that satisfies and the initial condition when

Evaluate the definite integral of the algebraic function. Use a graphing utility to verify your results.

The integrand of the following definite integral is a difference of two functions. Sketch the graph of the two functions and shade the region whose area is represented by the integral.

Use the Midpoint Rule with n = 4 to approximate the area of the following region.Round your answer to 3 decimal places.

Use formal substitution to find the indefinite integral

Use the Midpoint Rule n = 4 to approximate the area of the following region.

Find the area of the region bounded by the graphs. 1) 2)

Use the values and to evaluate the definite integral

Use the Midpoint Rule with to approximate the area of the region bounded by the graph of the function and the x-axis over the interval.Sketch the region.

Find the indefinite integral and check your result by differentiation.

Find the area of the region bounded by the graphs. 1) 2)

Functions, graphs, and Limits

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Techniques of Integration

Functions of Several Variables

Trigonometric Functions

Probability and Calculus

Series and Taylor Polynomials

Differential Equations

Filters

Exam 5: Integration and Its Applications

Use the Log Rule to find the indefinite integral for ​

Set up the definite integral that gives the area of the region bounded by the graphs. ​ ​ ​

Evaluate the integral ​

A ball is thrown vertically upwards from a height of 6 ft with an initial velocity of 40 ft per second. ​ How high will the ball go? ​

Evaluate the integral ​

Use algebra to rewrite the integrand; then integrate and simplify. ​ ​

Evaluate the integral ​

Find the indefinite integral. ​ ​

Find the supply function that satisfies and the initial condition when ​

Evaluate the definite integral of the algebraic function. ​ ​ Use a graphing utility to verify your results. ​

The integrand of the following definite integral is a difference of two functions. ​ ​ Sketch the graph of the two functions and shade the region whose area is represented by the integral. ​

Use the Midpoint Rule with n = 4 to approximate the area of the following region.Round your answer to 3 decimal places. ​ ​ ​

Use formal substitution to find the indefinite integral ​

Use the Midpoint Rule n = 4 to approximate the area of the following region. ​ ​ ​

Find the area of the region bounded by the graphs. ​ ​ 1) 2) ​

Use the values and to evaluate the definite integral ​

Use the Midpoint Rule with to approximate the area of the region bounded by the graph of the function and the x-axis over the interval.Sketch the region. ​ ​

Find the indefinite integral and check your result by differentiation. ​

Find the area of the region bounded by the graphs. ​ 1) 2) ​

Functions, graphs, and Limits

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Techniques of Integration

Functions of Several Variables

Trigonometric Functions

Probability and Calculus

Series and Taylor Polynomials

Differential Equations

Filters

Use the Log Rule to find the indefinite integral for

Set up the definite integral that gives the area of the region bounded by the graphs.

Evaluate the integral

A ball is thrown vertically upwards from a height of 6 ft with an initial velocity of 40 ft per second. How high will the ball go?

Evaluate the integral

Use algebra to rewrite the integrand; then integrate and simplify.

Evaluate the integral

Find the indefinite integral.

Find the supply function that satisfies and the initial condition when

Evaluate the definite integral of the algebraic function. Use a graphing utility to verify your results.

The integrand of the following definite integral is a difference of two functions. Sketch the graph of the two functions and shade the region whose area is represented by the integral.

Use the Midpoint Rule with n = 4 to approximate the area of the following region.Round your answer to 3 decimal places.

Use formal substitution to find the indefinite integral

Use the Midpoint Rule n = 4 to approximate the area of the following region.

Find the area of the region bounded by the graphs. 1) 2)

Use the values and to evaluate the definite integral

Use the Midpoint Rule with to approximate the area of the region bounded by the graph of the function and the x-axis over the interval.Sketch the region.

Find the indefinite integral and check your result by differentiation.

Find the area of the region bounded by the graphs. 1) 2)