Question 1

Find the indefinite integral. ​   ​

Accepted Answer

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

Question 2

Find the indefinite integral   . ​

Accepted Answer

A)    
B)    
C)    
D) 10 
E) none of the above 
A)    
B)    
C)    
D) 10 
E) none of the above

Question 3

Use sigma notation to write the sum   . ​

Accepted Answer

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

Question 4

Use the summation formulas to rewrite the expression   without the summation notation. ​

Accepted Answer

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

Question 5

Solve the differential equation. ​   ,   ​

Accepted Answer

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

Question 6

Find   given ​   .
​

Accepted Answer

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

Question 7

At   ,is the speed of the particle increasing or decreasing if   ? ​

Accepted Answer

A) ​decreasing 
B) ​increasing 
A) ​decreasing 
B) ​increasing

Question 8

The graph of f consists of line segments,as shown in the figure.Evaluate the definite integral   using geometric formulas. ​   ​

Accepted Answer

A) 4 
B) 3 
C) 1 
D) 2 
E) 5 
A) 4 
B) 3 
C) 1 
D) 2 
E) 5

Question 9

Initially a water tank contains 150 ft3.Water begins to drain from the tank at the rate of   cubic feet per hour.How many cubic feet of water will remain in the tank after 2 hours? Round your answer to three decimal places. ​

Accepted Answer

A) ​24.805 
B) ​125.195 
C) ​97.470 
D) ​52.530 
A) ​24.805 
B) ​125.195 
C) ​97.470 
D) ​52.530

Question 10

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

Accepted Answer

A)    
B)    
C) -1 
D) 1 
E) 0 
A)    
B)    
C) -1 
D) 1 
E) 0

Question 11

​What is   if   and   ? ​

Accepted Answer

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

Question 12

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

Accepted Answer

A) 5 
B) 7 
C) 6 
D) 4 
E) 8 
A) 5 
B) 7 
C) 6 
D) 4 
E) 8

Question 13

The maker of an automobile advertises that it takes 7 seconds to accelerate from 20 kilometers per hour to 90 kilometers per hour.Assuming constant acceleration,compute the acceleration in meters per second per second.Round your answer to three decimal places. ​

Accepted Answer

A) 1.944 m/sec2 
B) 4.365 m/sec2 
C) 6.250 m/sec2 
D) 3.056 m/sec2 
E) 2.778 m/sec2 
A) 1.944 m/sec2 
B) 4.365 m/sec2 
C) 6.250 m/sec2 
D) 3.056 m/sec2 
E) 2.778 m/sec2

Question 14

Find the area of the shaded region for the function   . ​   ​

Accepted Answer

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

Question 15

Find the average value of   on the interval   . ​

Accepted Answer

A)    
B) 35 
C)    
D)    
E) 40 
A)    
B) 35 
C)    
D)    
E) 40

Question 16

The graph of   ​ shown below consists of three line segments and one semicircle.Let   .Which of the following statements must be false? ​   ​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   has a relative maximum at
  
A) ​   
B) ​   
C) ​   
D) ​   has a relative maximum at

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

Find the area of the region bounded by the graphs of the equations   ,   ,   ,and   .Round your answer to four decimal places. ​

Accepted Answer

A) 15.2661 
B) 16.5423 
C) 16.2661 
D) 17.5423 
E) 16.8755 
A) 15.2661 
B) 16.5423 
C) 16.2661 
D) 17.5423 
E) 16.8755

Question 19

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 20

Find the indefinite integral   . ​

Accepted Answer

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

Find the indefinite integral.

Find the indefinite integral .

Use sigma notation to write the sum .

Use the summation formulas to rewrite the expression without the summation notation.

Solve the differential equation. ,

Find given .

At ,is the speed of the particle increasing or decreasing if ?

The graph of f consists of line segments,as shown in the figure.Evaluate the definite integral using geometric formulas.

Initially a water tank contains 150 ft³.Water begins to drain from the tank at the rate of cubic feet per hour.How many cubic feet of water will remain in the tank after 2 hours? Round your answer to three decimal places.

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

What is if and ?

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

The maker of an automobile advertises that it takes 7 seconds to accelerate from 20 kilometers per hour to 90 kilometers per hour.Assuming constant acceleration,compute the acceleration in meters per second per second.Round your answer to three decimal places.

Find the area of the shaded region for the function .

Find the average value of on the interval .

The graph of shown below consists of three line segments and one semicircle.Let .Which of the following statements must be false?

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

Find the area of the region bounded by the graphs of the equations , , ,and .Round your answer to four decimal places.

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

Find the indefinite integral .

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Differential Equations

Applications of Integration

Integration Techniques, L'Hôpital's Rule, and Improper Integrals

Infinite Series

Parametric Equations, Polar Coordinates, and Vectors

Mechanical Ventilation and Sedation: Assessment, Medications, and Complications

Filters

Exam 5: Integration

Find the indefinite integral. ​ ​

Find the indefinite integral . ​

Use sigma notation to write the sum . ​

Use the summation formulas to rewrite the expression without the summation notation. ​

Solve the differential equation. ​ , ​

Find given ​ . ​

At ,is the speed of the particle increasing or decreasing if ? ​

The graph of f consists of line segments,as shown in the figure.Evaluate the definite integral using geometric formulas. ​ ​

Initially a water tank contains 150 ft3.Water begins to drain from the tank at the rate of cubic feet per hour.How many cubic feet of water will remain in the tank after 2 hours? Round your answer to three decimal places. ​

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

​What is if and ? ​

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

The maker of an automobile advertises that it takes 7 seconds to accelerate from 20 kilometers per hour to 90 kilometers per hour.Assuming constant acceleration,compute the acceleration in meters per second per second.Round your answer to three decimal places. ​

Find the area of the shaded region for the function . ​ ​

Find the average value of on the interval . ​

The graph of ​ shown below consists of three line segments and one semicircle.Let .Which of the following statements must be false? ​ ​

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

Find the area of the region bounded by the graphs of the equations , , ,and .Round your answer to four decimal places. ​

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

Find the indefinite integral . ​

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Differential Equations

Applications of Integration

Integration Techniques, L'Hôpital's Rule, and Improper Integrals

Infinite Series

Parametric Equations, Polar Coordinates, and Vectors

Mechanical Ventilation and Sedation: Assessment, Medications, and Complications

Filters

Find the indefinite integral.

Find the indefinite integral .

Use sigma notation to write the sum .

Use the summation formulas to rewrite the expression without the summation notation.

Solve the differential equation. ,

Find given .

At ,is the speed of the particle increasing or decreasing if ?

The graph of f consists of line segments,as shown in the figure.Evaluate the definite integral using geometric formulas.

Initially a water tank contains 150 ft³.Water begins to drain from the tank at the rate of cubic feet per hour.How many cubic feet of water will remain in the tank after 2 hours? Round your answer to three decimal places.

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

What is if and ?

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

The maker of an automobile advertises that it takes 7 seconds to accelerate from 20 kilometers per hour to 90 kilometers per hour.Assuming constant acceleration,compute the acceleration in meters per second per second.Round your answer to three decimal places.

Find the area of the shaded region for the function .

Find the average value of on the interval .

The graph of shown below consists of three line segments and one semicircle.Let .Which of the following statements must be false?

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

Find the area of the region bounded by the graphs of the equations , , ,and .Round your answer to four decimal places.

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

Find the indefinite integral .