Question 1

Use integration tables to find the integral   . ​

Accepted Answer

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

Question 2

Find the indefinite integral by making the substitution   . ​   ​

Accepted Answer

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

Question 3

Use partial fractions to find   . ​

Accepted Answer

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

Question 4

Solve   . ​

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

Complete the square and find   . ​

Accepted Answer

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

Question 7

Apply the Extended Mean Value Theorem to the functions   and   on the interval   ,and find all values c in the interval   such that   . ​

Accepted Answer

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

Question 8

Use integration tables to evaluate the integral   . ​

Accepted Answer

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

Question 9

Find the definite integral. ​   ​

Accepted Answer

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

Question 10

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

Accepted Answer

A)      
B)    
C)    
D) 0 
E)      
A)      
B)    
C)    
D) 0 
E)

Question 11

Find the indefinite integral by making the substitution   . ​   ​

Accepted Answer

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

Question 12

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

Accepted Answer

A)    
B)    
C) 1 
D)    
E)    
A)    
B)    
C) 1 
D)    
E)

Question 13

Use integration tables to find   . ​

Accepted Answer

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

Question 14

Find the indefinite integral. ​   ​

Accepted Answer

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

Question 15

Find the indefinite integral by making the substitution   . ​   ​

Accepted Answer

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

Question 16

Use a table of integrals to find the integral.   ​

Accepted Answer

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

Question 17

Determine whether the improper integral   diverges or converges.Evaluate the integral if it converges. ​

Accepted Answer

A)    
B)    
A)    
B)

Question 18

Determine whether the improper integral   diverges or converges. ​

Accepted Answer

A)    
B)    
A)    
B)

Question 19

​What is the area of the region in the first quadrant between the   -axis,the graph   ,and   ? ​   ​

Accepted Answer

A) ​1 
B) ​2 
C) ​0 
D) ​∞ 
A) ​1 
B) ​2 
C) ​0 
D) ​∞

Question 20

Find   . ​

Accepted Answer

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

Use integration tables to find the integral .

Find the indefinite integral by making the substitution .

Use partial fractions to find $Use partial fractions to find . $ .

Solve .

Find the indefinite integral.

Complete the square and find .

Apply the Extended Mean Value Theorem to the functions and on the interval ,and find all values c in the interval such that .

Use integration tables to evaluate the integral .

Find the definite integral.

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

Find the indefinite integral by making the substitution .

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

Use integration tables to find .

Find the indefinite integral.

Find the indefinite integral by making the substitution .

Use a table of integrals to find the integral.

Determine whether the improper integral diverges or converges.Evaluate the integral if it converges.

Determine whether the improper integral diverges or converges.

What is the area of the region in the first quadrant between the -axis,the graph ,and ?

Find .

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Infinite Series

Parametric Equations, Polar Coordinates, and Vectors

Mechanical Ventilation and Sedation: Assessment, Medications, and Complications

Filters

Exam 8: Integration Techniques, L'Hôpital's Rule, and Improper Integrals

Use integration tables to find the integral . ​

Find the indefinite integral by making the substitution . ​ ​

Use partial fractions to find . ​

Solve . ​

Find the indefinite integral. ​ ​

Complete the square and find . ​

Apply the Extended Mean Value Theorem to the functions and on the interval ,and find all values c in the interval such that . ​

Use integration tables to evaluate the integral . ​

Find the definite integral. ​ ​

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

Find the indefinite integral by making the substitution . ​ ​

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

Use integration tables to find . ​

Find the indefinite integral. ​ ​

Find the indefinite integral by making the substitution . ​ ​

Use a table of integrals to find the integral. ​

Determine whether the improper integral diverges or converges.Evaluate the integral if it converges. ​

Determine whether the improper integral diverges or converges. ​

​What is the area of the region in the first quadrant between the -axis,the graph ,and ? ​ ​

Find . ​

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Infinite Series

Parametric Equations, Polar Coordinates, and Vectors

Mechanical Ventilation and Sedation: Assessment, Medications, and Complications

Filters

Use integration tables to find the integral .

Find the indefinite integral by making the substitution .

Use partial fractions to find $Use partial fractions to find . $ .

Solve .

Find the indefinite integral.

Complete the square and find .

Apply the Extended Mean Value Theorem to the functions and on the interval ,and find all values c in the interval such that .

Use integration tables to evaluate the integral .

Find the definite integral.

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

Find the indefinite integral by making the substitution .

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

Use integration tables to find .

Find the indefinite integral.

Find the indefinite integral by making the substitution .

Use a table of integrals to find the integral.

Determine whether the improper integral diverges or converges.Evaluate the integral if it converges.

Determine whether the improper integral diverges or converges.

What is the area of the region in the first quadrant between the -axis,the graph ,and ?

Find .