Question 1

Find the indefinite integral of the following function and check the result by differentiation. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)  none of the above 
A)    
B)    
C)    
D)    
E)  none of the above

Question 2

Evaluate the definite integral of the algebraic function. ​   ​
Use a graphing utility to verify your results.Round your answer to 4 decimal places.
​

Accepted Answer

A)  4.2422 
B)  5.4526 
C)  -4.2422 
D)  1.0439 
E)  0.7140 
A)  4.2422 
B)  5.4526 
C)  -4.2422 
D)  1.0439 
E)  0.7140

Question 3

The graph of the derivative of a function is given below.Sketch the graphs of two functions that have the given derivative. ​   ​

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 4

An evergreen nursery sells a certain shrub after 8 years.The growth rate of the shrub is given by   ,where t is the time in years and h is the height in centimeters.The seedlings are 18 centimeters tall when planted (t = 0).How tall are the shrubs when they are sold? ​

Accepted Answer

A)  72 centimeters 
B)  67 centimeters 
C)  78 centimeters 
D)  162 centimeters 
E)  274 centimeters 
A)  72 centimeters 
B)  67 centimeters 
C)  78 centimeters 
D)  162 centimeters 
E)  274 centimeters

Question 5

Find the indefinite integral. ​   ​

Accepted Answer

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

Question 6

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 7

Identify u and   for the integral   ​

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

Estimate the surface area of the oil spill shown in the figure using the Midpoint Rule. ​   ​

Accepted Answer

A)  ≈ 481.6 mi2 
B)  ≈ 301.6 mi2 
C)  ≈ 311.6 mi2 
D)  ≈ 431.6 mi2 
E)  ≈ 381.6 mi2 
A)  ≈ 481.6 mi2 
B)  ≈ 301.6 mi2 
C)  ≈ 311.6 mi2 
D)  ≈ 431.6 mi2 
E)  ≈ 381.6 mi2

Question 10

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

Accepted Answer

A)  3 
B)  8 
C)  2 
D)  1 
E)  6 
A)  3 
B)  8 
C)  2 
D)  1 
E)  6

Question 11

The rate of depreciation of a building is given by   dollars per year,   Use the definite integral to find the total depreciation over the first 10 years. ​

Accepted Answer

A)  $260,000 
B)  $26,000 
C)  $130,000 
D)  $13,487 
E)  $520,000 
A)  $260,000 
B)  $26,000 
C)  $130,000 
D)  $13,487 
E)  $520,000

Question 12

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

Accepted Answer

A)  2.5 
B)  1.2 
C)  1.5 
D)  1.9 
E)  2.3 
A)  2.5 
B)  1.2 
C)  1.5 
D)  1.9 
E)  2.3

Question 13

Find the indefinite integral. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)  none of the above 
A)    
B)    
C)    
D)    
E)  none of the above

Question 14

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 15

Find the indefinite integral. ​   ​

Accepted Answer

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

Question 16

Find the equation of the function f whose graph passes through the point   and whose derivative is   ​

Accepted Answer

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

Question 17

Find the indefinite integral of the following function and check the result by differentiation. ​   ​

Accepted Answer

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

Question 18

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)  0.556 
B)  0.436 
C)  0.673 
D)  0.268 
E)  0.883 
A)  0.556 
B)  0.436 
C)  0.673 
D)  0.268 
E)  0.883

Question 19

Evaluate the integral   ​

Accepted Answer

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

Question 20

Find the cost function for the marginal cost   and fixed cost of $2,800 (for x = 0). ​

Accepted Answer

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

Find the indefinite integral of the following function and check the result by differentiation.

Evaluate the definite integral of the algebraic function. Use a graphing utility to verify your results.Round your answer to 4 decimal places.

The graph of the derivative of a function is given below.Sketch the graphs of two functions that have the given derivative.

An evergreen nursery sells a certain shrub after 8 years.The growth rate of the shrub is given by ,where t is the time in years and h is the height in centimeters.The seedlings are 18 centimeters tall when planted (t = 0).How tall are the shrubs when they are sold?

Find the indefinite integral.

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.

Identify u and for the integral

Find the indefinite integral and check your result by differentiation.

Estimate the surface area of the oil spill shown in the figure using the Midpoint Rule.

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

The rate of depreciation of a building is given by dollars per year, Use the definite integral to find the total depreciation over the first 10 years.

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

Find the indefinite integral.

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.

Find the indefinite integral.

Find the equation of the function f whose graph passes through the point and whose derivative is

Find the indefinite integral of the following function and check the result by differentiation.

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

Evaluate the integral

Find the cost function for the marginal cost and fixed cost of $2,800 (for x = 0).

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

Find the indefinite integral of the following function and check the result by differentiation. ​ ​

Evaluate the definite integral of the algebraic function. ​ ​ Use a graphing utility to verify your results.Round your answer to 4 decimal places. ​

The graph of the derivative of a function is given below.Sketch the graphs of two functions that have the given derivative. ​ ​

An evergreen nursery sells a certain shrub after 8 years.The growth rate of the shrub is given by ,where t is the time in years and h is the height in centimeters.The seedlings are 18 centimeters tall when planted (t = 0).How tall are the shrubs when they are sold? ​

Find the indefinite integral. ​ ​

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. ​

Identify u and for the integral ​

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

Estimate the surface area of the oil spill shown in the figure using the Midpoint Rule. ​ ​

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

The rate of depreciation of a building is given by dollars per year, Use the definite integral to find the total depreciation over the first 10 years. ​

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

Find the indefinite integral. ​ ​

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. ​

Find the indefinite integral. ​ ​

Find the equation of the function f whose graph passes through the point and whose derivative is ​

Find the indefinite integral of the following function and check the result by differentiation. ​ ​

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

Evaluate the integral ​

Find the cost function for the marginal cost and fixed cost of $2,800 (for x = 0). ​

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

Find the indefinite integral of the following function and check the result by differentiation.

Evaluate the definite integral of the algebraic function. Use a graphing utility to verify your results.Round your answer to 4 decimal places.

The graph of the derivative of a function is given below.Sketch the graphs of two functions that have the given derivative.

An evergreen nursery sells a certain shrub after 8 years.The growth rate of the shrub is given by ,where t is the time in years and h is the height in centimeters.The seedlings are 18 centimeters tall when planted (t = 0).How tall are the shrubs when they are sold?

Find the indefinite integral.

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.

Identify u and for the integral

Find the indefinite integral and check your result by differentiation.

Estimate the surface area of the oil spill shown in the figure using the Midpoint Rule.

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

The rate of depreciation of a building is given by dollars per year, Use the definite integral to find the total depreciation over the first 10 years.

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

Find the indefinite integral.

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.

Find the indefinite integral.

Find the equation of the function f whose graph passes through the point and whose derivative is

Find the indefinite integral of the following function and check the result by differentiation.

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

Evaluate the integral

Find the cost function for the marginal cost and fixed cost of $2,800 (for x = 0).