Question 1

Verify that   has a removable discontinuity at   , define   such that   is continuous at   , and estimate   by   .

Accepted Answer

The answer of Verify that   has a removable...

Question 2

Evaluate the following integral using trigonometric identities and reduction formulas.

Accepted Answer

The answer of Evaluate the following integral using trigonometric identities...

Question 3

Compute the integral   ..

Accepted Answer

The answer of Compute the integral   .....

Question 4

Evaluate the integral   .

Accepted Answer

The answer of Evaluate the integral   ....

Question 5

Evaluate the integrals.
A)   
B)

Accepted Answer

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

Question 6

Compute the integral   .

Accepted Answer

The answer of Compute the integral   ....

Question 7

Evaluate the following improper integrals.
A)   
B)

Accepted Answer

The answer of Evaluate the following improper integrals.
A)  ...

Question 8

The partial fraction decomposition of   is:

Accepted Answer

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

Question 9

Use the Trapezoidal Rule to determine the average number of customers in the store during a 2-hour interval if the number of customers recorded at 10-minute intervals are   .

Accepted Answer

The answer of Use the Trapezoidal Rule to determine the...

Question 10

Evaluate the integral   .

Accepted Answer

The answer of Evaluate the integral   ....

Question 11

Calculate   and   for the following. 
A)   
B)

Accepted Answer

The answer of Calculate   and   for...

Question 12

Evaluate the following improper integrals.
A)   
B)

Accepted Answer

The answer of Evaluate the following improper integrals.
A)  ...

Question 13

Which of the following methods is efficient in computing the integral   ?

Accepted Answer

A)  Substitution Method with   
B)  Integration by Parts with   and   
C)  Integration by Parts with   and   
D)  Integration by Parts with   and   
E)  None of the techniques covered so far is efficient. 
A)  Substitution Method with   
B)  Integration by Parts with   and   
C)  Integration by Parts with   and   
D)  Integration by Parts with   and   
E)  None of the techniques covered so far is efficient.

Question 14

Evaluate the following integrals.
A)   
B)

Accepted Answer

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

Question 15

Use the substitution   and the identities   to evaluate the integral   .

Accepted Answer

The answer of Use the substitution   and the...

Question 16

Which of the following integrals converges?

Accepted Answer

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

Question 17

Compute the following integrals.
A)   
B)

Accepted Answer

The answer of Compute the following integrals.
A)   
B)...

Question 18

Evaluate the integral   .

Accepted Answer

The answer of Evaluate the integral   ....

Question 19

The value of the integral   is:

Accepted Answer

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

Question 20

Find   such that   approximates   with an error of at most   .

Accepted Answer

The answer of Find   such that  ...

Verify that has a removable discontinuity at , define such that is continuous at , and estimate by .

Evaluate the following integral using trigonometric identities and reduction formulas.

Compute the integral ..

Evaluate the integral .

Evaluate the integrals. A) B)

Compute the integral .

Evaluate the following improper integrals. A) B)

The partial fraction decomposition of $The partial fraction decomposition of is:$ is:

Use the Trapezoidal Rule to determine the average number of customers in the store during a 2-hour interval if the number of customers recorded at 10-minute intervals are .

Evaluate the integral .

Calculate and for the following. A) B)

Evaluate the following improper integrals. A) B)

Which of the following methods is efficient in computing the integral ?

Evaluate the following integrals. A) B)

Use the substitution and the identities to evaluate the integral .

Which of the following integrals converges?

Compute the following integrals. A) B)

Evaluate the integral .

The value of the integral is:

Find such that approximates with an error of at most .

Precalculus Review

Limits

Differentiation

Applications of the Derivative

The Integral

Applications of the Integral

Exponential Functions

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 8: Techniques of Integration

Verify that has a removable discontinuity at , define such that is continuous at , and estimate by .

Evaluate the following integral using trigonometric identities and reduction formulas.

Compute the integral ..

Evaluate the integral .

Evaluate the integrals. A) B)

Compute the integral .

Evaluate the following improper integrals. A) B)

The partial fraction decomposition of is:

Use the Trapezoidal Rule to determine the average number of customers in the store during a 2-hour interval if the number of customers recorded at 10-minute intervals are .

Evaluate the integral .

Calculate and for the following. A) B)

Evaluate the following improper integrals. A) B)

Which of the following methods is efficient in computing the integral ?

Evaluate the following integrals. A) B)

Use the substitution and the identities to evaluate the integral .

Which of the following integrals converges?

Compute the following integrals. A) B)

Evaluate the integral .

The value of the integral is:

Find such that approximates with an error of at most .

Precalculus Review

Limits

Differentiation

Applications of the Derivative

The Integral

Applications of the Integral

Exponential Functions

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

The partial fraction decomposition of $The partial fraction decomposition of is:$ is: