Question 1

The graph of   is obtained by reflecting the graph of   through   .   Let   and   denote the area in the figure. The following equality holds:

Accepted Answer

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

Question 2

Compute   and   over   using the following values.                   1.2
.75
.4       2.5

Accepted Answer

The answer of Compute   and   over...

Question 3

Evaluate the following integrals:
A)   
B)   
C)

Accepted Answer

The answer of Evaluate the following integrals:
A)   
B)...

Question 4

Use the substitution   to evaluate the integral   .

Accepted Answer

The answer of Use the substitution   to evaluate...

Question 5

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

Accepted Answer

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

Question 6

Evaluate   .

Accepted Answer

The answer of Evaluate   ....

Question 7

Find the net change in velocity over   with acceleration   ft/sec2.

Accepted Answer

Question 8

Solve the initial value problem   .

Accepted Answer

The answer of Solve the initial value problem  ...

Question 9

Find the displacement over the time interval   of a car whose velocity is given by   ft/sec.

Accepted Answer

The answer of Find the displacement over the time interval...

Question 10

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

Accepted Answer

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

Question 11

Solve the initial value problem   .

Accepted Answer

The answer of Solve the initial value problem  ...

Question 12

Compute the area under the graph of   over   as the limit of   as   .

Accepted Answer

The answer of Compute the area under the graph of...

Question 13

Evaluate the following limits using L'Hopital's Rule and the Fundamental Theorem of Calculus, Part II:
A)   
B)

Accepted Answer

The answer of Evaluate the following limits using L'Hopital's Rule...

Question 14

Calculate   , where   .

Accepted Answer

The answer of Calculate   , where  ...

Question 15

Let   be the area of the trapezoid shown in the figure. 
A) Evaluate the right-endpoint approximation   . 
B) Compute the area   using geometry and verify   .

Accepted Answer

The answer of Let   be the area of...

Question 16

Match the approximation with the corresponding function

Accepted Answer

a) E; b) B

Question 17

Use a trigonometric identity to evaluate the integral   .

Accepted Answer

The answer of Use a trigonometric identity to evaluate the...

Question 18

The substitution   leads to which integration formula below?

Accepted Answer

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

Question 19

is equal to which of the following integrals?

Accepted Answer

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

Question 20

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

Accepted Answer

The answer of Evaluate the following definite integrals using substitution:
A)...

The graph of is obtained by reflecting the graph of through . Let and denote the area in the figure. The following equality holds:

Compute and over using the following values. 1.2 .75 .4 2.5

Evaluate the following integrals: A) B) C)

Use the substitution to evaluate the integral .

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

Evaluate .

Find the net change in velocity over with acceleration ft/sec².

Solve the initial value problem .

Find the displacement over the time interval of a car whose velocity is given by ft/sec.

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

Solve the initial value problem .

Compute the area under the graph of over as the limit of as .

Evaluate the following limits using L'Hopital's Rule and the Fundamental Theorem of Calculus, Part II: A) B)

Calculate , where .

Let be the area of the trapezoid shown in the figure. A) Evaluate the right-endpoint approximation . B) Compute the area using geometry and verify .

Match the approximation with the corresponding function

Use a trigonometric identity to evaluate the integral .

The substitution leads to which integration formula below?

is equal to which of the following integrals?

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

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

The graph of is obtained by reflecting the graph of through . Let and denote the area in the figure. The following equality holds:

Compute and over using the following values. 1.2 .75 .4 2.5

Evaluate the following integrals: A) B) C)

Use the substitution to evaluate the integral .

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

Evaluate .

Find the net change in velocity over with acceleration ft/sec2.

Solve the initial value problem .

Find the displacement over the time interval of a car whose velocity is given by ft/sec.

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

Solve the initial value problem .

Compute the area under the graph of over as the limit of as .

Evaluate the following limits using L'Hopital's Rule and the Fundamental Theorem of Calculus, Part II: A) B)

Calculate , where .

Let be the area of the trapezoid shown in the figure. A) Evaluate the right-endpoint approximation . B) Compute the area using geometry and verify .

Match the approximation with the corresponding function

Use a trigonometric identity to evaluate the integral .

The substitution leads to which integration formula below?

is equal to which of the following integrals?

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

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

Find the net change in velocity over with acceleration ft/sec².