Question 1

Evaluate the integral   ​

Accepted Answer

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

Question 2

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

Accepted Answer

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

Question 3

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 4

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

Accepted Answer

A)  2 
B)  3 
C)  4 
D)  6 
E)  1 
A)  2 
B)  3 
C)  4 
D)  6 
E)  1

Question 5

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 6

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 7

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 8

Estimate the surface area of the golf green shown in the figure using the midpoint rule. ​   ​

Accepted Answer

A)  966 
B)  161 
C)  1449 
D)  1550 
E)  234 
A)  966 
B)  161 
C)  1449 
D)  1550 
E)  234

Question 9

The marginal cost of a product is modeled by   ,when x = 8,C = 9.Find the cost function. ​

Accepted Answer

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

Question 10

Evaluate the following definite integral. ​   ​
Use a graphing utility to check your answer.
​

Accepted Answer

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

Question 11

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 12

Sketch the region whose area is given by the definite integral and then use a geometric formula to evaluate the integral. ​   ​

Accepted Answer

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

Question 13

Estimate the surface area of the golf green shown in the figure using the midpoint rule. ​   ​

Accepted Answer

A)  780 
B)  156 
C)  1404 
D)  1502 
E)  524 
A)  780 
B)  156 
C)  1404 
D)  1502 
E)  524

Question 14

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

Accepted Answer

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

Question 15

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 16

Find a function that satisfies the conditions   ,   ,   ​

Accepted Answer

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

Question 17

Find the indefinite integral 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 18

Find the average value of the function over the given interval. ​   on   ​

Accepted Answer

A)  -31 
B)  -93 
C)  -30.2 
D)  -29.8 
E)  42.6 
A)  -31 
B)  -93 
C)  -30.2 
D)  -29.8 
E)  42.6

Question 19

Use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the graph of   and the x-axis over the interval   Round your answer to 4 decimal places. ​

Accepted Answer

A)  2.8958 
B)  3.1244 
C)  4.0389 
D)  3.9246 
E)  3.8103 
A)  2.8958 
B)  3.1244 
C)  4.0389 
D)  3.9246 
E)  3.8103

Question 20

Two models,   and   ,are given for revenue (in billions of dollars per year)for a large corporation.Both models are estimates of revenues for 2007 through 2011,with t = 7 corresponding to 2007.Which model is projecting the greater revenue? How much more total revenue does that model project over the five-year period? ​

Accepted Answer

A)  The model   projects greater revenue than   $16.56 billion 
B)  The model   projects greater revenue than   $14.40 billion 
C)  The model   projects greater revenue than   $18.00 billion 
D)  The model   projects greater revenue than   $17.10 billion 
E)  The model   projects greater revenue than   $16.74 billion 
A)  The model   projects greater revenue than   $16.56 billion 
B)  The model   projects greater revenue than   $14.40 billion 
C)  The model   projects greater revenue than   $18.00 billion 
D)  The model   projects greater revenue than   $17.10 billion 
E)  The model   projects greater revenue than   $16.74 billion

Evaluate the integral

Find the indefinite integral and check the result by differentiation.

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

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

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

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

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

Estimate the surface area of the golf green shown in the figure using the midpoint rule.

The marginal cost of a product is modeled by ,when x = 8,C = 9.Find the cost function.

Evaluate the following definite integral. Use a graphing utility to check your answer.

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

Sketch the region whose area is given by the definite integral and then use a geometric formula to evaluate the integral.

Estimate the surface area of the golf green shown in the figure using the midpoint rule.

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

Identify u and for the integral

Find a function that satisfies the conditions , ,

Find the indefinite integral and check the result by differentiation.

Find the average value of the function over the given interval. on

Use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the graph of and the x-axis over the interval Round your answer to 4 decimal places.

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

Evaluate the integral ​

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

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

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

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

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

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

Estimate the surface area of the golf green shown in the figure using the midpoint rule. ​ ​

The marginal cost of a product is modeled by ,when x = 8,C = 9.Find the cost function. ​

Evaluate the following definite integral. ​ ​ Use a graphing utility to check your answer. ​

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

Sketch the region whose area is given by the definite integral and then use a geometric formula to evaluate the integral. ​ ​

Estimate the surface area of the golf green shown in the figure using the midpoint rule. ​ ​

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

Identify u and for the integral ​

Find a function that satisfies the conditions , , ​

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

Find the average value of the function over the given interval. ​ on ​

Use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the graph of and the x-axis over the interval Round your answer to 4 decimal places. ​

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

Evaluate the integral

Find the indefinite integral and check the result by differentiation.

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

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

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

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

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

Estimate the surface area of the golf green shown in the figure using the midpoint rule.

The marginal cost of a product is modeled by ,when x = 8,C = 9.Find the cost function.

Evaluate the following definite integral. Use a graphing utility to check your answer.

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

Sketch the region whose area is given by the definite integral and then use a geometric formula to evaluate the integral.

Estimate the surface area of the golf green shown in the figure using the midpoint rule.

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

Identify u and for the integral

Find a function that satisfies the conditions , ,

Find the indefinite integral and check the result by differentiation.

Find the average value of the function over the given interval. on

Use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the graph of and the x-axis over the interval Round your answer to 4 decimal places.