Question 1

The integral   dx is convergent.

Accepted Answer

A) True 
 B)False

Question 2

The integral   dx is convergent.

Accepted Answer

A) True 
 B)False

Question 3

Evaluate, if convergent,   dx.

Accepted Answer

A)  2 $\pi$ 
B)  $\pi$ 
C)  1 
D)  0 
E)  divergent 
A)  2 $\pi$ 
B)  $\pi$ 
C)  1 
D)  0 
E)  divergent

Question 4

Integrate   dx.

Accepted Answer

A)  6 - 2e 
B)  4e - 6 
C)  e + 3 
D)  4e - 3 
E)  2e - 1 
A)  6 - 2e 
B)  4e - 6 
C)  e + 3 
D)  4e - 3 
E)  2e - 1

Question 5

Evaluate   .

Accepted Answer

A)  x   (x) -   ln(1 +   ) + C 
B)    + C 
C)  x   (x) -   ln(1 +   ) + C 
D)  arc   + C 
E)  ln   + C 
A)  x   (x) -   ln(1 +   ) + C 
B)    + C 
C)  x   (x) -   ln(1 +   ) + C 
D)  arc   + C 
E)  ln   + C

Question 6

Which of the following is not an improper integral?

Accepted Answer

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

Question 7

The integral   dx is convergent.

Accepted Answer

A) True 
 B)False

Question 8

The Midpoint Rule   is used to estimate the value of   dx with an absolute error not exceeding 0.0003. Find the smallest number of sub intervals n.

Accepted Answer

A)  17 
B)  34 
C)  49 
D)  25 
E)  27 
A)  17 
B)  34 
C)  49 
D)  25 
E)  27

Question 9

Evaluate the Trapezoid and Midpoint Rule approximations   and   for   dx. Round your answer to 4 decimal places.

Accepted Answer

A)    = 0.6354;   = 0.6305 
B)    = 0.6305;   = 0.6354 
C)    = 0.5304;   = 0.5263 
D)    = 0.6367;   = 0.6298 
E)    = 0.6376;   = 0.6287 
A)    = 0.6354;   = 0.6305 
B)    = 0.6305;   = 0.6354 
C)    = 0.5304;   = 0.5263 
D)    = 0.6367;   = 0.6298 
E)    = 0.6376;   = 0.6287

Question 10

Evaluate   dx.

Accepted Answer

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

Question 11

Evaluate the integral   dx.

Accepted Answer

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

Question 12

Let   (x) be the Maclaurin polynomial of degree n for the function   , and let   . Calculate (to 9 decimal places) A8 and A9 and quote an approximate value for   to a precision you feel is justified by those values.

Accepted Answer

A₈ ≈ 0.7468

Question 13

Let F(x) =   Use Maple or another computer algebra program to compute F(x) and an approximate value for F(   ) correct to 5 decimal places.

Accepted Answer

A)  F(x) =       FresnelS   ; F(   ) $\approx$ 0.89480 
B)  F(x) =       FresnelS   ; F(   ) $\approx$ 0.89483 
C)  F(x) =       FresnelS   ; F(   ) $\approx$ 0.89486 
D)  F(x) =       FresnelS   ; F(   ) $\approx$ 0.89489 
E)  F(x) =       FresnelS   ; F(   ) $\approx$ 0.894878 
A)  F(x) =       FresnelS   ; F(   ) $\approx$ 0.89480 
B)  F(x) =       FresnelS   ; F(   ) $\approx$ 0.89483 
C)  F(x) =       FresnelS   ; F(   ) $\approx$ 0.89486 
D)  F(x) =       FresnelS   ; F(   ) $\approx$ 0.89489 
E)  F(x) =       FresnelS   ; F(   ) $\approx$ 0.894878

Question 14

Evaluate the integral   dx.

Accepted Answer

A)  4 ln   - ln   + C 
B)  4 ln   + ln   + C 
C)  4 ln   + ln   + C 
D)  4 ln   - ln   + C 
E)  2 ln   - ln   + C 
A)  4 ln   - ln   + C 
B)  4 ln   + ln   + C 
C)  4 ln   + ln   + C 
D)  4 ln   - ln   + C 
E)  2 ln   - ln   + C

Question 15

Evaluate   dx.

Accepted Answer

A)  16$\pi$ 
B)  8$\pi$ 
C)    
D)  16$\pi$ - 8 
E)  12$\pi$ 
A)  16$\pi$ 
B)  8$\pi$ 
C)    
D)  16$\pi$ - 8 
E)  12$\pi$

Question 16

Evaluate   dx.

Accepted Answer

A)    -   
B)    -   
C)    -   
D)    -   
E)    +   
A)    -   
B)    -   
C)    -   
D)    -   
E)    +

Question 17

The correct form of the partial fraction decomposition for the function   is given by

Accepted Answer

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

Question 18

Evaluate   .

Accepted Answer

A)    ln   -   -   + C 
B)  -   ln   -   +   + C 
C)  -   ln   -   -   + C 
D)    ln   -   +   + C 
E)    ln   -   -   + C 
A)    ln   -   -   + C 
B)  -   ln   -   +   + C 
C)  -   ln   -   -   + C 
D)    ln   -   +   + C 
E)    ln   -   -   + C

Question 19

Evaluate   dx.

Accepted Answer

A)    + a ln   + C 
B)    - a ln   + C 
C)    - a ln   + C 
D)    + a ln   + C 
E)    - ln   + C 
A)    + a ln   + C 
B)    - a ln   + C 
C)    - a ln   + C 
D)    + a ln   + C 
E)    - ln   + C

Question 20

Find   dx.

Accepted Answer

A)  1 -   
B)  -1 
C)    - 1 
D)    
E)  -1 -   
A)  1 -   
B)  -1 
C)    - 1 
D)    
E)  -1 -

The integral dx is convergent.

The integral dx is convergent.

Evaluate, if convergent, dx.

Integrate dx.

Evaluate .

Which of the following is not an improper integral?

The integral dx is convergent.

The Midpoint Rule is used to estimate the value of dx with an absolute error not exceeding 0.0003. Find the smallest number of sub intervals n.

Evaluate the Trapezoid and Midpoint Rule approximations and for dx. Round your answer to 4 decimal places.

Evaluate dx.

Evaluate the integral dx.

Let (x) be the Maclaurin polynomial of degree n for the function , and let . Calculate (to 9 decimal places) A₈ and A₉ and quote an approximate value for to a precision you feel is justified by those values.

Let F(x) = Use Maple or another computer algebra program to compute F(x) and an approximate value for F( ) correct to 5 decimal places.

Evaluate the integral dx.

Evaluate dx.

Evaluate dx.

The correct form of the partial fraction decomposition for the function $The correct form of the partial fraction decomposition for the function is given by$ is given by

Evaluate .

Evaluate dx.

Find dx.

Preliminaries

Limits and Continuity

Differentiation

Transcendental Functions

More Applications of Differentiation

Integration

Applications of Integration

Conics, Parametric Curves, and Polar Curves

Sequences, Series, and Power Series

Vectors and Coordinate Geometry in 3-Space

Vector Functions and Curves

Partial Differentiation

Applications of Partial Derivatives

Multiple Integration

Vector Fields

Vector Calculus

Differential Forms and Exterior Calculus

Ordinary Differential Equations

Filters

Exam 7: Techniques of Integration

The integral dx is convergent.

The integral dx is convergent.

Evaluate, if convergent, dx.

Integrate dx.

Evaluate .

Which of the following is not an improper integral?

The integral dx is convergent.

The Midpoint Rule is used to estimate the value of dx with an absolute error not exceeding 0.0003. Find the smallest number of sub intervals n.

Evaluate the Trapezoid and Midpoint Rule approximations and for dx. Round your answer to 4 decimal places.

Evaluate dx.

Evaluate the integral dx.

Let (x) be the Maclaurin polynomial of degree n for the function , and let . Calculate (to 9 decimal places) A8 and A9 and quote an approximate value for to a precision you feel is justified by those values.

Let F(x) = Use Maple or another computer algebra program to compute F(x) and an approximate value for F( ) correct to 5 decimal places.

Evaluate the integral dx.

Evaluate dx.

Evaluate dx.

The correct form of the partial fraction decomposition for the function is given by

Evaluate .

Evaluate dx.

Find dx.

Preliminaries

Limits and Continuity

Differentiation

Transcendental Functions

More Applications of Differentiation

Integration

Applications of Integration

Conics, Parametric Curves, and Polar Curves

Sequences, Series, and Power Series

Vectors and Coordinate Geometry in 3-Space

Vector Functions and Curves

Partial Differentiation

Applications of Partial Derivatives

Multiple Integration

Vector Fields

Vector Calculus

Differential Forms and Exterior Calculus

Ordinary Differential Equations

Filters

Let (x) be the Maclaurin polynomial of degree n for the function , and let . Calculate (to 9 decimal places) A₈ and A₉ and quote an approximate value for to a precision you feel is justified by those values.

The correct form of the partial fraction decomposition for the function $The correct form of the partial fraction decomposition for the function is given by$ is given by