Question 1

Let   be the area under   over   .
Which of the following is correct?

Accepted Answer

A)    , hence   . 
B)    , hence   . 
C)    , hence   . 
D)    , hence   . 
E)  None of the above. 
A)    , hence   . 
B)    , hence   . 
C)    , hence   . 
D)    , hence   . 
E)  None of the above. C

Question 2

The area between the   -axis and the graph of   on   is.

Accepted Answer

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

Question 3

Find   and   if   and   .

Accepted Answer

The answer of Find   and   if...

Question 4

Evaluate the following definite integrals using the indicated substitution:
A)   
B)   
C)

Accepted Answer

The answer of Evaluate the following definite integrals using the...

Question 5

A particle moves in a straight line with velocity   ft/sec. Find the displacement over the interval   .

Accepted Answer

The answer of A particle moves in a straight line...

Question 6

Calculate   for the function   over   .

Accepted Answer

The answer of Calculate   for the function ...

Question 7

Calculate   to five decimal places for   over   .

Accepted Answer

The answer of Calculate   to five decimal places...

Question 8

Evaluate the integral   .

Accepted Answer

The answer of Evaluate the integral   ....

Question 9

Using the global extrema of   on   , find   and   such that

Accepted Answer

The answer of Using the global extrema of  ...

Question 10

The Mean Value Theorem and the Comparison Theorem imply that

Accepted Answer

A)    for   and   . 
B)    for   and   . 
C)    for   and   . 
D)    for   and   . 
E)  None of the above. 
A)    for   and   . 
B)    for   and   . 
C)    for   and   . 
D)    for   and   . 
E)  None of the above.

Question 11

Calculate the following sums:
A)   
B)   
C)

Accepted Answer

The answer of Calculate the following sums:
A)   
B)...

Question 12

The substitution   leads to which integration formula?

Accepted Answer

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

Question 13

The function   that satisfies the equality   is:

Accepted Answer

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

Question 14

Let   be the function shown in the figure:     Given that:   and   
A) Find the constants   and   . 
B) Determine the cumulative area function   , and give the value   .

Accepted Answer

The answer of Let   be the function shown...

Question 15

Find the area under the graph of   over the interval   by computing   . The area is

Accepted Answer

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

Question 16

Use the change of variables formula to evaluate the following definite integrals:
A)   
B)   
C)

Accepted Answer

The answer of Use the change of variables formula to...

Question 17

Let   be a twice differentiable function. The integral equation   can be written as the following initial value problem:

Accepted Answer

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

Question 18

Let   ,   ,   and   Calculate the following
(A   (B   (C

Accepted Answer

The answer of Let   ,   ,...

Question 19

The substitution   and the identity   lead to which of the following integration formulas?

Accepted Answer

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

Question 20

Which of the following is true about

Accepted Answer

A)  It does not exist since the one-sided limits are different. 
B)  It exists and equals 1. 
C)  It exists and equals 0. 
D)  It cannot be computed by L'Hopital's Rule since the conditions for using the rule are not satisfied. 
E)  It exists and equals   
A)  It does not exist since the one-sided limits are different. 
B)  It exists and equals 1. 
C)  It exists and equals 0. 
D)  It cannot be computed by L'Hopital's Rule since the conditions for using the rule are not satisfied. 
E)  It exists and equals

Let be the area under over . Which of the following is correct?

The area between the -axis and the graph of on is.

Find and if and .

Evaluate the following definite integrals using the indicated substitution: A) B) C)

A particle moves in a straight line with velocity ft/sec. Find the displacement over the interval .

Calculate for the function over .

Calculate to five decimal places for over .

Evaluate the integral .

Using the global extrema of on , find and such that

The Mean Value Theorem and the Comparison Theorem imply that

Calculate the following sums: A) B) C)

The substitution leads to which integration formula?

The function that satisfies the equality is:

Let be the function shown in the figure: Given that: and A) Find the constants and . B) Determine the cumulative area function , and give the value .

Find the area under the graph of over the interval by computing . The area is

Use the change of variables formula to evaluate the following definite integrals: A) B) C)

Let be a twice differentiable function. The integral equation can be written as the following initial value problem:

Let , , and Calculate the following (A (B (C

The substitution and the identity lead to which of the following integration formulas?

Which of the following is true about

Precalculus Review

Limits

Differentiation

Applications of the Derivative

Applications of the Integral

Exponential Functions

Techniques of Integration

Further Applications of the Integral and Taylor Polynomials

Introduction to Differential Equations

Infinite Series

Parametric Equations, Polar Coordinates, and Conic Sections

Vector Geometry

Calculus of Vector-Valued Functions

Differentiation in Several Variables

Multiple Integration

Line and Surface Integrals

Fundamental Theorems of Vector Analysis

Filters

Exam 5: The Integral

Let be the area under over . Which of the following is correct?

The area between the -axis and the graph of on is.

Find and if and .

Evaluate the following definite integrals using the indicated substitution: A) B) C)

A particle moves in a straight line with velocity ft/sec. Find the displacement over the interval .

Calculate for the function over .

Calculate to five decimal places for over .

Evaluate the integral .

Using the global extrema of on , find and such that

The Mean Value Theorem and the Comparison Theorem imply that

Calculate the following sums: A) B) C)

The substitution leads to which integration formula?

The function that satisfies the equality is:

Let be the function shown in the figure: Given that: and A) Find the constants and . B) Determine the cumulative area function , and give the value .

Find the area under the graph of over the interval by computing . The area is

Use the change of variables formula to evaluate the following definite integrals: A) B) C)

Let be a twice differentiable function. The integral equation can be written as the following initial value problem:

Let , , and Calculate the following (A (B (C

The substitution and the identity lead to which of the following integration formulas?

Which of the following is true about

Precalculus Review

Limits

Differentiation

Applications of the Derivative

Applications of the Integral

Exponential Functions

Techniques of Integration

Further Applications of the Integral and Taylor Polynomials

Introduction to Differential Equations

Infinite Series

Parametric Equations, Polar Coordinates, and Conic Sections

Vector Geometry

Calculus of Vector-Valued Functions

Differentiation in Several Variables

Multiple Integration

Line and Surface Integrals

Fundamental Theorems of Vector Analysis

Filters