Question 1

Find the area of the region bounded by the graphs of the algebraic functions. ​     ​

Accepted Answer

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

Question 2

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

Accepted Answer

A)  -20 
B)  100 
C)  -100 
D)  20 
E)  7 
A)  -20 
B)  100 
C)  -100 
D)  20 
E)  7 D

Question 3

Estimate the surface area of the pond shown in the figure using the Midpoint Rule. ​   ​

Accepted Answer

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

Question 4

Find the area of the region bounded by the graphs of the algebraic functions. ​
​     ​

Accepted Answer

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

Question 5

Evaluate the integral   ​

Accepted Answer

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

Question 6

Evaluate the definite integral   ​

Accepted Answer

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

Question 7

Find the area of the region bounded by the graphs. ​   1)   2)   ​

Accepted Answer

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

Question 8

Find the particular solution that satisfies the differential equation   and initial condition   ​

Accepted Answer

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

Question 9

Evaluate the integral   ​

Accepted Answer

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

Question 10

Find the average value of the function over the given interval. ​   on   ​

Accepted Answer

A)    
B)    
C)    
D)  25 
E)    
A)    
B)    
C)    
D)  25 
E)

Question 11

Evaluate the integral   ​

Accepted Answer

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

Question 12

Estimate the surface area of the golf green shown in the figure using the midpoint rule. ​   ​

Accepted Answer

A)  636 
B)  159 
C)  1431 
D)  1561 
E)  644 
A)  636 
B)  159 
C)  1431 
D)  1561 
E)  644

Question 13

Find the indefinite integral of the following function and check the result by differentiation. ​   ​

Accepted Answer

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

Question 14

Find the area of the region bounded by the graphs. ​   1)   2)   ​

Accepted Answer

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

Question 15

Determine the area of the given region. ​   ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)  None of the above 
A)    
B)    
C)    
D)    
E)  None of the above

Question 16

Evaluate the integral   ​

Accepted Answer

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

Question 17

The graph of the derivative of a function is given below.Sketch the graphs of two functions that have the given derivative. ​   ​

Accepted Answer

A)  ​  
​1:  
2:   
B)  ​  
1:   ​
2:   
C)  ​   ​1:  
2:   
D)  ​   ​1:  
2:   
E)  ​  
1:  
2:   
A)  ​  
​1:  
2:   
B)  ​  
1:   ​
2:   
C)  ​   ​1:  
2:   
D)  ​   ​1:  
2:   
E)  ​  
1:  
2:

Question 18

Find the indefinite integral. ​   ​

Accepted Answer

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

Question 19

Evaluate the integral   ​

Accepted Answer

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

Question 20

Find the indefinite integral. ​   ​

Accepted Answer

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

Find the area of the region bounded by the graphs of the algebraic functions.

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

Estimate the surface area of the pond shown in the figure using the Midpoint Rule.

Find the area of the region bounded by the graphs of the algebraic functions.

Evaluate the integral

Evaluate the definite integral

Find the area of the region bounded by the graphs. 1) 2)

Find the particular solution that satisfies the differential equation and initial condition

Evaluate the integral

Find the average value of the function over the given interval. on

Evaluate the integral

Estimate the surface area of the golf green shown in the figure using the midpoint rule.

Find the indefinite integral of the following function and check the result by differentiation.

Find the area of the region bounded by the graphs. 1) 2)

Determine the area of the given region.

Evaluate the integral

The graph of the derivative of a function is given below.Sketch the graphs of two functions that have the given derivative.

Find the indefinite integral.

Evaluate the integral

Find the indefinite integral.

Functions, graphs, and Limits

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Techniques of Integration

Functions of Several Variables

Trigonometric Functions

Probability and Calculus

Series and Taylor Polynomials

Differential Equations

Filters

Exam 5: Integration and Its Applications

Find the area of the region bounded by the graphs of the algebraic functions. ​ ​

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

Estimate the surface area of the pond shown in the figure using the Midpoint Rule. ​ ​

Find the area of the region bounded by the graphs of the algebraic functions. ​ ​ ​

Evaluate the integral ​

Evaluate the definite integral ​

Find the area of the region bounded by the graphs. ​ 1) 2) ​

Find the particular solution that satisfies the differential equation and initial condition ​

Evaluate the integral ​

Find the average value of the function over the given interval. ​ on ​

Evaluate the integral ​

Estimate the surface area of the golf green shown in the figure using the midpoint rule. ​ ​

Find the indefinite integral of the following function and check the result by differentiation. ​ ​

Find the area of the region bounded by the graphs. ​ 1) 2) ​

Determine the area of the given region. ​ ​ ​

Evaluate the integral ​

The graph of the derivative of a function is given below.Sketch the graphs of two functions that have the given derivative. ​ ​

Find the indefinite integral. ​ ​

Evaluate the integral ​

Find the indefinite integral. ​ ​

Functions, graphs, and Limits

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Techniques of Integration

Functions of Several Variables

Trigonometric Functions

Probability and Calculus

Series and Taylor Polynomials

Differential Equations

Filters

Find the area of the region bounded by the graphs of the algebraic functions.

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

Estimate the surface area of the pond shown in the figure using the Midpoint Rule.

Find the area of the region bounded by the graphs of the algebraic functions.

Evaluate the integral

Evaluate the definite integral

Find the area of the region bounded by the graphs. 1) 2)

Find the particular solution that satisfies the differential equation and initial condition

Evaluate the integral

Find the average value of the function over the given interval. on

Evaluate the integral

Estimate the surface area of the golf green shown in the figure using the midpoint rule.

Find the indefinite integral of the following function and check the result by differentiation.

Find the area of the region bounded by the graphs. 1) 2)

Determine the area of the given region.

Evaluate the integral

The graph of the derivative of a function is given below.Sketch the graphs of two functions that have the given derivative.

Find the indefinite integral.

Evaluate the integral

Find the indefinite integral.