Question 1

Evaluate the definite integral. ​   ​

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Question 2

Find the indefinite integral. ​   ​

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Question 3

Evaluate the integral   . ​

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Question 4

Find   given   . ​

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Question 5

Find   . ​

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Question 6

The rate of change in sales S is inversely proportional to time   measured in weeks.Find S as a function of t if sales after 2 and 4 weeks are 250 units and 450 units respectively. ​

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Question 7

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

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Question 8

Find the indefinite integral of the following function. ​   ​​

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Question 9

The rate of depreciation   of a machine is inversely proportional to the square of   where V is the value of the machine t years after it was purchased.The initial value of the machine was $500,000 and its value decreased $100,000 in the first year.Estimate its value after 4 years.Round your answer to the nearest integer. ​

Accepted Answer

A) $233,333 
B) $133,333 
C) $466,666 
D) $566,667 
E) $500,000 
A) $233,333 
B) $133,333 
C) $466,666 
D) $566,667 
E) $500,000

Question 10

Use the differential equation   and the initial condition   to find y. ​

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Question 11

Solve the differential equation. ​   ,   ​

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Question 12

Find the time required for an object to cool from 340°F to 240°F by evaluating   ,where t is time in minutes.Round your answer to four decimal places. ​

Accepted Answer

A) 7.3417 minutes 
B) 5.0489 minutes 
C) 4.2110 minutes 
D) 4.6321 minutes 
E) 6.6742 minutes 
A) 7.3417 minutes 
B) 5.0489 minutes 
C) 4.2110 minutes 
D) 4.6321 minutes 
E) 6.6742 minutes

Question 13

Find the position of the particle at any time t ​if   cm/sec and   .

Accepted Answer

The answer of Find the position of the particle at...

Question 14

Evaluate   . ​

Accepted Answer

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A) ​   
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Question 15

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) -26.5 
B) 6 
C) 44 
D) 105.5 
E) -30.5 
A) -26.5 
B) 6 
C) 44 
D) 105.5 
E) -30.5

Question 16

Find the area of the region bounded by the graphs of the equations   ,   ,   .Round your answer to the nearest whole number. ​

Accepted Answer

A) 320 
B) 15 
C) 81 
D) 13 
E) 6 
A) 320 
B) 15 
C) 81 
D) 13 
E) 6

Question 17

Solve the differential equation. ​   ​

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Question 18

Use the differential equation   and the initial condition   to find y. ​

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Question 19

Find the indefinite integral   . ​

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Question 20

Find the indefinite integral   . ​

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Evaluate the definite integral.

Find the indefinite integral.

Evaluate the integral .

Find given .

Find .

The rate of change in sales S is inversely proportional to time measured in weeks.Find S as a function of t if sales after 2 and 4 weeks are 250 units and 450 units respectively.

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

Find the indefinite integral of the following function.

Use the differential equation and the initial condition to find y.

Solve the differential equation. ,

Find the time required for an object to cool from 340°F to 240°F by evaluating ,where t is time in minutes.Round your answer to four decimal places.

Find the position of the particle at any time t if cm/sec and .

Evaluate .

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.

Find the area of the region bounded by the graphs of the equations , , .Round your answer to the nearest whole number.

Solve the differential equation.

Use the differential equation and the initial condition to find y.

Find the indefinite integral .

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

Evaluate the definite integral. ​ ​

Find the indefinite integral. ​ ​

Evaluate the integral . ​

Find given . ​

Find . ​

The rate of change in sales S is inversely proportional to time measured in weeks.Find S as a function of t if sales after 2 and 4 weeks are 250 units and 450 units respectively. ​

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

Find the indefinite integral of the following function. ​ ​​

Use the differential equation and the initial condition to find y. ​

Solve the differential equation. ​ , ​

Find the time required for an object to cool from 340°F to 240°F by evaluating ,where t is time in minutes.Round your answer to four decimal places. ​

Find the position of the particle at any time t ​if cm/sec and .

Evaluate . ​

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. ​ ​

Find the area of the region bounded by the graphs of the equations , , .Round your answer to the nearest whole number. ​

Solve the differential equation. ​ ​

Use the differential equation and the initial condition to find y. ​

Find the indefinite integral . ​

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

Evaluate the definite integral.

Find the indefinite integral.

Evaluate the integral .

Find given .

Find .

The rate of change in sales S is inversely proportional to time measured in weeks.Find S as a function of t if sales after 2 and 4 weeks are 250 units and 450 units respectively.

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

Find the indefinite integral of the following function.

Use the differential equation and the initial condition to find y.

Solve the differential equation. ,

Find the time required for an object to cool from 340°F to 240°F by evaluating ,where t is time in minutes.Round your answer to four decimal places.

Find the position of the particle at any time t if cm/sec and .

Evaluate .

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.

Find the area of the region bounded by the graphs of the equations , , .Round your answer to the nearest whole number.

Solve the differential equation.

Use the differential equation and the initial condition to find y.

Find the indefinite integral .

Find the indefinite integral .