Question 1

Find   given ​   .
​

Accepted Answer

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

Question 2

Find the indefinite integral   . ​

Accepted Answer

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

Question 3

What is the average value of ​   for the closed interval   ? ​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
A) ​   
B) ​   
C) ​   
D) ​

Question 4

Write the limit   ,as a definite integral on the interval   where   is any point in the   subinterval. ​

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

The diagram below shows upper and lower sums for the function   using 4 subintervals.Use upper and lower sums to approximate the area of the region using the 4 subintervals.Round to three decimal places.

Accepted Answer

A) lower: 1.518 ;upper: 1.768 
B) lower: 6.072 ;upper: 7.072 
C) lower: 3.036 ;upper: 3.536 
D) lower: 1.268 ;upper: 2.018 
A) lower: 1.518 ;upper: 1.768 
B) lower: 6.072 ;upper: 7.072 
C) lower: 3.036 ;upper: 3.536 
D) lower: 1.268 ;upper: 2.018

Question 7

Find the indefinite integral   . ​

Accepted Answer

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

Question 8

Find   if   . ​

Accepted Answer

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

Question 9

Evaluate the definite integral. ​   ​

Accepted Answer

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

Question 10

Determine the area of the given region. ​   ​   ​

Accepted Answer

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

Question 11

Find the indefinite integral   . ​

Accepted Answer

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

Question 12

Find the indefinite integral   . ​

Accepted Answer

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

Question 13

​If   ,what is   ​

Accepted Answer

A) ​   
B) ​   
C) ​12 
D) ​36 
A) ​   
B) ​   
C) ​12 
D) ​36

Question 14

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

Accepted Answer

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

Question 15

Write the following limit as a definite integral on the interval   where   is any point in the   subinterval. ​   ​

Accepted Answer

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

Question 16

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

Accepted Answer

A) -30 
B) -9 
C) 9 
D) -16 
E) 15 
A) -30 
B) -9 
C) 9 
D) -16 
E) 15

Question 17

Find the indefinite integral of   . ​

Accepted Answer

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

Question 18

Find the limit of   as   . ​   ​

Accepted Answer

A) 0 
B) unbounded 
C)    
D) 1 
E)    
A) 0 
B) unbounded 
C)    
D) 1 
E)

Question 19

Write the limit   ,as a definite integral on the interval   ,where   is any point in the   subinterval. ​

Accepted Answer

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

Question 20

Evaluate the following definite integral by the limit definition. ​   ​

Accepted Answer

A) -124 
B) 136 
C) -136 
D) 112 
E) 124 
A) -124 
B) 136 
C) -136 
D) 112 
E) 124

Find given .

Find the indefinite integral .

What is the average value of for the closed interval ?

Write the limit ,as a definite integral on the interval where is any point in the subinterval.

Find the indefinite integral .

The diagram below shows upper and lower sums for the function using 4 subintervals.Use upper and lower sums to approximate the area of the region using the 4 subintervals.Round to three decimal places.

Find the indefinite integral .

Find if .

Evaluate the definite integral.

Determine the area of the given region.

Find the indefinite integral .

Find the indefinite integral .

If ,what is

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

Write the following limit as a definite integral on the interval where is any point in the subinterval.

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

Find the indefinite integral of .

Find the limit of as .

Write the limit ,as a definite integral on the interval ,where is any point in the subinterval.

Evaluate the following definite integral by the limit definition.

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 given ​ . ​

Find the indefinite integral . ​

What is the average value of ​ for the closed interval ? ​

Write the limit ,as a definite integral on the interval where is any point in the subinterval. ​

Find the indefinite integral . ​

The diagram below shows upper and lower sums for the function using 4 subintervals.Use upper and lower sums to approximate the area of the region using the 4 subintervals.Round to three decimal places.

Find the indefinite integral . ​

Find if . ​

Evaluate the definite integral. ​ ​

Determine the area of the given region. ​ ​ ​

Find the indefinite integral . ​

Find the indefinite integral . ​

​If ,what is ​

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

Write the following limit as a definite integral on the interval where is any point in the subinterval. ​ ​

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

Find the indefinite integral of . ​

Find the limit of as . ​ ​

Write the limit ,as a definite integral on the interval ,where is any point in the subinterval. ​

Evaluate the following definite integral by the limit definition. ​ ​

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 given .

Find the indefinite integral .

What is the average value of for the closed interval ?

Write the limit ,as a definite integral on the interval where is any point in the subinterval.

Find the indefinite integral .

Find the indefinite integral .

Find if .

Evaluate the definite integral.

Determine the area of the given region.

Find the indefinite integral .

Find the indefinite integral .

If ,what is

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

Write the following limit as a definite integral on the interval where is any point in the subinterval.

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

Find the indefinite integral of .

Find the limit of as .

Write the limit ,as a definite integral on the interval ,where is any point in the subinterval.

Evaluate the following definite integral by the limit definition.