Question 1

Find the indefinite integral of   . ​

Accepted Answer

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

Question 2

Find   . ​

Accepted Answer

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

Question 3

Evaluate the limit   using L'Hopital's Rule if necessary. ​

Accepted Answer

A)    
B)    
C)  1 
D)  0 
E)  does not exist 
A)    
B)    
C)  1 
D)  0 
E)  does not exist

Question 4

Find   . ​

Accepted Answer

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

Question 5

Find the indefinite integral. ​   ​

Accepted Answer

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

Question 6

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 7

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. Write an equation that gives the population at any time t. ​

Accepted Answer

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

Question 8

Determine the area of the given region. ​   ​   ​

Accepted Answer

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

Question 9

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

Accepted Answer

A)  -198.5 
B)  10 
C)  102.5 
D)  109 
E)  -199.5 
A)  -198.5 
B)  10 
C)  102.5 
D)  109 
E)  -199.5

Question 10

Find the integral   . ​

Accepted Answer

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

Question 11

Find the indefinite integral of the following function. ​   ​

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

Find the indefinite integral   . ​

Accepted Answer

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

Question 14

Solve the differential equation. ​   ​

Accepted Answer

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

Question 15

Evaluate the integral. ​   ​
Given,
​   ,   ,   ,   .
​

Accepted Answer

A)  -156 
B)  15 
C)  -6,628 
D)  -7,646 
E)  -154 
A)  -156 
B)  15 
C)  -6,628 
D)  -7,646 
E)  -154

Question 16

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

Accepted Answer

A)  2,400 
B)  189,660 
C)  193,575 
D)  759,075 
E)  191,400 
A)  2,400 
B)  189,660 
C)  193,575 
D)  759,075 
E)  191,400

Question 17

Suppose the demand equation for a product is   . Find the average price p on the interval   . Round your answer to the nearest dollar. ​

Accepted Answer

A)  $5 
B)  $164 
C)  $114 
D)  $1,120 
E)  $103 
A)  $5 
B)  $164 
C)  $114 
D)  $1,120 
E)  $103

Question 18

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

Accepted Answer

A)  3 
B)  5 
C)  4 
D)  2 
E)  6 
A)  3 
B)  5 
C)  4 
D)  2 
E)  6

Question 19

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 20

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 400 units respectively.

Accepted Answer

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

Find the indefinite integral of .

Find .

Evaluate the limit using L'Hopital's Rule if necessary.

Find .

Find the indefinite integral.

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

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. Write an equation that gives the population at any time t.

Determine the area of the given region.

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

Find the integral .

Find the indefinite integral of the following function.

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

Find the indefinite integral .

Solve the differential equation.

Evaluate the integral. Given, , , , .

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

Suppose the demand equation for a product is . Find the average price p on the interval . Round your answer to the nearest dollar.

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

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

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 400 units respectively.

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Differential Equations

Applications of Integration

Integration Techniques and Improper Integrals

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

Exam 5: Integration

Find the indefinite integral of . ​

Find . ​

Evaluate the limit using L'Hopital's Rule if necessary. ​

Find . ​

Find the indefinite integral. ​ ​

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

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. Write an equation that gives the population at any time t. ​

Determine the area of the given region. ​ ​ ​

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

Find the integral . ​

Find the indefinite integral of the following function. ​ ​

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

Find the indefinite integral . ​

Solve the differential equation. ​ ​

Evaluate the integral. ​ ​ Given, ​ , , , . ​

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

Suppose the demand equation for a product is . Find the average price p on the interval . Round your answer to the nearest dollar. ​

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

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

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 400 units respectively.

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Differential Equations

Applications of Integration

Integration Techniques and Improper Integrals

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

Find the indefinite integral of .

Find .

Evaluate the limit using L'Hopital's Rule if necessary.

Find .

Find the indefinite integral.

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

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. Write an equation that gives the population at any time t.

Determine the area of the given region.

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

Find the integral .

Find the indefinite integral of the following function.

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

Find the indefinite integral .

Solve the differential equation.

Evaluate the integral. Given, , , , .

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

Suppose the demand equation for a product is . Find the average price p on the interval . Round your answer to the nearest dollar.

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