Question 1

Find the indefinite integral. ​   ​

Accepted Answer

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

Question 2

The oscillating current in an electrical circuit is   where I is measured in amperes and t is measured in seconds.Find the average current for the time interval   .Round your answer to three decimal places. ​

Accepted Answer

A) 1.691 amps 
B) 0.691 amps 
C) 1.382 amps 
D) 2.765 amps 
E) 2.382 amps 
A) 1.691 amps 
B) 0.691 amps 
C) 1.382 amps 
D) 2.765 amps 
E) 2.382 amps

Question 3

Find the indefinite integral. ​   ​

Accepted Answer

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

Question 4

The height above the ground of an object thrown upward from a point   feet above the ground with an initial velocity of   feet per second is given by the function   .A balloon,rising vertically with a velocity of 32 feet per second,releases a sandbag at the instant it is 12 feet above the ground.At what velocity will it hit the ground? Round your answer to three decimal places. ​

Accepted Answer

A) -60.284 ft/sec 
B) -42.332 ft/sec 
C) -15.071 ft/sec 
D) 64.985 ft/sec 
E) 74.332 ft/sec 
A) -60.284 ft/sec 
B) -42.332 ft/sec 
C) -15.071 ft/sec 
D) 64.985 ft/sec 
E) 74.332 ft/sec

Question 5

Find the solution of the differential equation   which passes through the point   . ​

Accepted Answer

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

Question 6

The rate of disbursement   of a 2 million dollar federal grant is proportional to the square of   .Time t is measured in days   and Q is the amount that remains to be disbursed.Find the amount that remains to be disbursed after 30 days.Assume that all the money will be disbursed in 100 days. ​

Accepted Answer

A) $686,000 
B) $50,700 
C) $101,400 
D) $33,800 
E) $1,029,000 
A) $686,000 
B) $50,700 
C) $101,400 
D) $33,800 
E) $1,029,000

Question 7

Sketch the region whose area is given by the definite integral and then use a geometric formula to evaluate the integral.Round to one decimal place if necessary. ​   ​

Accepted Answer

A) 8 
B) 9 
C) 9.5 
D) 16 
E) 52.5 
A) 8 
B) 9 
C) 9.5 
D) 16 
E) 52.5

Question 8

Use the properties of summation and Theorem 5.2 to evaluate the sum. ​   ​

Accepted Answer

A) 1,744 
B) 246,512 
C) 248,992 
D) 985,552 
E) 247,504 
A) 1,744 
B) 246,512 
C) 248,992 
D) 985,552 
E) 247,504

Question 9

On the closed interval [0,3],what is the velocity of the particle when its acceleration is at a maximum? Round your answer to three decimal places.

Accepted Answer

The answer of On the closed interval [0,3],what is the...

Question 10

Find the integral   . ​

Accepted Answer

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

Question 11

Use left endpoints and 6 rectangles to find the approximation of the area of the region between the graph of the function   and the x-axis over the interval   .Round your answer to four decimal places. ​

Accepted Answer

A) 0.0036 
B) 0.0736 
C) 0.0636 
D) 0.0436 
E) -0.0264 
A) 0.0036 
B) 0.0736 
C) 0.0636 
D) 0.0436 
E) -0.0264

Question 12

Find the solution of the differential equation   which passes through the point   . ​

Accepted Answer

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

Question 13

Suppose a population of bacteria is changing at a rate of   ,where t is the time in days.The initial population (when   )is 2,000.Identify an equation that gives the population at any time t and use it to find the population when   days.Round your answer to the nearest integer. ​

Accepted Answer

A) 3,423 
B) 3,718 
C) 4,423 
D) 2,717 
E) 3,717 
A) 3,423 
B) 3,718 
C) 4,423 
D) 2,717 
E) 3,717

Question 14

Find the indefinite integral of the following function. ​   ​

Accepted Answer

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

Question 15

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

Accepted Answer

A) -76 
B) -26 
C) 74 
D) 124 
E) -126 
A) -76 
B) -26 
C) 74 
D) 124 
E) -126

Question 16

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

Accepted Answer

A) -11 
B) 10 
C) -14 
D) -28 
E) -6 
A) -11 
B) 10 
C) -14 
D) -28 
E) -6

Question 17

Evaluate the definite integral. ​   ​

Accepted Answer

A) 13 
B)    
C)    
D)    
E) 3 
A) 13 
B)    
C)    
D)    
E) 3

Question 18

The sales S (in thousands of units)of a seasonal product are given by the model   where t is the time in months,with   corresponding to January.Find the average sales for the first quarter   .Round your answer to three decimal places. ​

Accepted Answer

A) 89.903 thousand units 
B) 91.145 thousand units 
C) 100.387 thousand units 
D) 128.213 thousand units 
E) 71.537 thousand units 
A) 89.903 thousand units 
B) 91.145 thousand units 
C) 100.387 thousand units 
D) 128.213 thousand units 
E) 71.537 thousand units

Question 19

Evaluate   . ​

Accepted Answer

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

Question 20

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

Accepted Answer

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

Find the indefinite integral.

The oscillating current in an electrical circuit is where I is measured in amperes and t is measured in seconds.Find the average current for the time interval .Round your answer to three decimal places.

Find the indefinite integral.

Find the solution of the differential equation which passes through the point .

The rate of disbursement of a 2 million dollar federal grant is proportional to the square of .Time t is measured in days and Q is the amount that remains to be disbursed.Find the amount that remains to be disbursed after 30 days.Assume that all the money will be disbursed in 100 days.

Sketch the region whose area is given by the definite integral and then use a geometric formula to evaluate the integral.Round to one decimal place if necessary.

Use the properties of summation and Theorem 5.2 to evaluate the sum.

On the closed interval [0,3],what is the velocity of the particle when its acceleration is at a maximum? Round your answer to three decimal places.

Find the integral .

Use left endpoints and 6 rectangles to find the approximation of the area of the region between the graph of the function and the x-axis over the interval .Round your answer to four decimal places.

Find the solution of the differential equation which passes through the point .

Suppose a population of bacteria is changing at a rate of ,where t is the time in days.The initial population (when )is 2,000.Identify an equation that gives the population at any time t and use it to find the population when days.Round your answer to the nearest integer.

Find the indefinite integral of the following function.

Find the average value of the function over the interval .

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

Evaluate the definite integral.

The sales S (in thousands of units)of a seasonal product are given by the model where t is the time in months,with corresponding to January.Find the average sales for the first quarter .Round your answer to three decimal places.

Evaluate .

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

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. ​ ​

The oscillating current in an electrical circuit is where I is measured in amperes and t is measured in seconds.Find the average current for the time interval .Round your answer to three decimal places. ​

Find the indefinite integral. ​ ​

Find the solution of the differential equation which passes through the point . ​

The rate of disbursement of a 2 million dollar federal grant is proportional to the square of .Time t is measured in days and Q is the amount that remains to be disbursed.Find the amount that remains to be disbursed after 30 days.Assume that all the money will be disbursed in 100 days. ​

Sketch the region whose area is given by the definite integral and then use a geometric formula to evaluate the integral.Round to one decimal place if necessary. ​ ​

Use the properties of summation and Theorem 5.2 to evaluate the sum. ​ ​

On the closed interval [0,3],what is the velocity of the particle when its acceleration is at a maximum? Round your answer to three decimal places.

Find the integral . ​

Use left endpoints and 6 rectangles to find the approximation of the area of the region between the graph of the function and the x-axis over the interval .Round your answer to four decimal places. ​

Find the solution of the differential equation which passes through the point . ​

Suppose a population of bacteria is changing at a rate of ,where t is the time in days.The initial population (when )is 2,000.Identify an equation that gives the population at any time t and use it to find the population when days.Round your answer to the nearest integer. ​

Find the indefinite integral of the following function. ​ ​

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

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

Evaluate the definite integral. ​ ​

The sales S (in thousands of units)of a seasonal product are given by the model where t is the time in months,with corresponding to January.Find the average sales for the first quarter .Round your answer to three decimal places. ​

Evaluate . ​

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

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.

The oscillating current in an electrical circuit is where I is measured in amperes and t is measured in seconds.Find the average current for the time interval .Round your answer to three decimal places.

Find the indefinite integral.

Find the solution of the differential equation which passes through the point .

The rate of disbursement of a 2 million dollar federal grant is proportional to the square of .Time t is measured in days and Q is the amount that remains to be disbursed.Find the amount that remains to be disbursed after 30 days.Assume that all the money will be disbursed in 100 days.

Sketch the region whose area is given by the definite integral and then use a geometric formula to evaluate the integral.Round to one decimal place if necessary.

Use the properties of summation and Theorem 5.2 to evaluate the sum.

Find the integral .

Use left endpoints and 6 rectangles to find the approximation of the area of the region between the graph of the function and the x-axis over the interval .Round your answer to four decimal places.

Find the solution of the differential equation which passes through the point .

Suppose a population of bacteria is changing at a rate of ,where t is the time in days.The initial population (when )is 2,000.Identify an equation that gives the population at any time t and use it to find the population when days.Round your answer to the nearest integer.

Find the indefinite integral of the following function.

Find the average value of the function over the interval .

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

Evaluate the definite integral.

The sales S (in thousands of units)of a seasonal product are given by the model where t is the time in months,with corresponding to January.Find the average sales for the first quarter .Round your answer to three decimal places.

Evaluate .

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