Question 1

Evaluate the definite integral. ​  ​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 2

Find the indefinite integral. ​  ​

Accepted Answer

A)   
B)    
C)   
D)   
E)

Question 3

Evaluate the integral  . ​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 4

Find  given  . ​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 5

Find  . ​

Accepted Answer

A)   
B)   
C)   
D)   
E)

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. ​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 7

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)

Question 8

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

Accepted Answer

A)   
B)   
C)   
D)   
E)

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

Question 10

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

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 11

Solve the differential equation. ​  ,  ​

Accepted Answer

A)   
B)   
C)   
D)   
E)

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

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

A) ​  
B) ​  
C) ​  
D) ​

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

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

Question 17

Solve the differential equation. ​  ​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 18

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

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 19

Find the indefinite integral  . ​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 20

Find the indefinite integral  . ​

Accepted Answer

A)   
B)   
C)   
D)   
E)

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 .

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 . ​

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 .