Question 1

Integrate the function.
-  dx

Accepted Answer

A)  3 ln   + C 
B)    + C 
C)  3   + C 
D)  3   + C 
A)  3 ln   + C 
B)    + C 
C)  3   + C 
D)  3   + C

Question 2

Evaluate the integral.
-

Accepted Answer

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

Question 3

Express the integrand as a sum of partial fractions and evaluate the integral.
-   dx

Accepted Answer

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

Question 4

Integrate the function.
-  , x > 4

Accepted Answer

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

Question 5

Evaluate the integral by making a substitution and then using a table of integrals.
-

Accepted Answer

A)  ln   - sin t + C 
B)  ln   + cos t + C 
C)  ln   + sin t + C 
D)  ln   - sin t + C 
A)  ln   - sin t + C 
B)  ln   + cos t + C 
C)  ln   + sin t + C 
D)  ln   - sin t + C

Question 6

Use reduction formulas to evaluate the integral.
-

Accepted Answer

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

Question 7

Use reduction formulas to evaluate the integral.
-

Accepted Answer

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

Question 8

Express the integrand as a sum of partial fractions and evaluate the integral.
-  dx

Accepted Answer

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

Question 9

Evaluate the integral.
-

Accepted Answer

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

Question 10

Evaluate the integral.
-

Accepted Answer

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

Question 11

Evaluate the improper integral or state that it is divergent.
-

Accepted Answer

A)  Divergent 
B)  1.569 
C)  0.121 
D)  -1.569 
A)  Divergent 
B)  1.569 
C)  0.121 
D)  -1.569

Question 12

Choose the one alternative that best completes the statement or answers the question. Evaluate the integral
-

Accepted Answer

A)  7 
B)  2   
C)  8 
D)  11 
A)  7 
B)  2   
C)  8 
D)  11

Question 13

Choose the one alternative that best completes the statement or answers the question. Evaluate the integral
-

Accepted Answer

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

Question 14

Evaluate the integral.
-

Accepted Answer

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

Question 15

Evaluate the improper integral or state that it is divergent.
-

Accepted Answer

A)  8$\pi$   
B)  16 ln   
C)  8$\pi$ 
D)  8   
A)  8$\pi$   
B)  16 ln   
C)  8$\pi$ 
D)  8

Question 16

Choose the one alternative that best completes the statement or answers the question. Evaluate the integral
-

Accepted Answer

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

Question 17

Integrate the function.
-  dy

Accepted Answer

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

Question 18

Determine whether the integral converges or diverges.
-

Accepted Answer

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

Question 19

Express the integrand as a sum of partial fractions and evaluate the integral.
-

Accepted Answer

A)  2.37 
B)  1.33 
C)  -1.18 
D)  1.18 
A)  2.37 
B)  1.33 
C)  -1.18 
D)  1.18

Question 20

Evaluate the integral.
-

Accepted Answer

A)  0 
B)    
C)    
D)    
A)  0 
B)    
C)    
D)

Integrate the function. - dx

Evaluate the integral. -

Express the integrand as a sum of partial fractions and evaluate the integral. - $Express the integrand as a sum of partial fractions and evaluate the integral. - dx$ dx

Integrate the function. - , x > 4

Evaluate the integral by making a substitution and then using a table of integrals. -

Use reduction formulas to evaluate the integral. -

Use reduction formulas to evaluate the integral. -

Express the integrand as a sum of partial fractions and evaluate the integral. - $Express the integrand as a sum of partial fractions and evaluate the integral. - dx$ dx

Evaluate the integral. -

Evaluate the integral. -

Evaluate the improper integral or state that it is divergent. -

Choose the one alternative that best completes the statement or answers the question. Evaluate the integral -

Choose the one alternative that best completes the statement or answers the question. Evaluate the integral -

Evaluate the integral. -

Evaluate the improper integral or state that it is divergent. -

Choose the one alternative that best completes the statement or answers the question. Evaluate the integral -

Integrate the function. - dy

Determine whether the integral converges or diverges. -

Express the integrand as a sum of partial fractions and evaluate the integral. - $Express the integrand as a sum of partial fractions and evaluate the integral. -$

Evaluate the integral. -

Functions

Limits

Derivatives

Applications of the Derivative

Integration

Applications of Integration

Logarithmic, Exponential, and Hyperbolic Functions

Differential Equations

Sequences and Infinite Series

Power Series

Parametric and Polar Curves

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Calculus

Filters

Exam 8: Integration Techniques

Integrate the function. - dx

Evaluate the integral. -

Express the integrand as a sum of partial fractions and evaluate the integral. - dx

Integrate the function. - , x > 4

Evaluate the integral by making a substitution and then using a table of integrals. -

Use reduction formulas to evaluate the integral. -

Use reduction formulas to evaluate the integral. -

Express the integrand as a sum of partial fractions and evaluate the integral. - dx

Evaluate the integral. -

Evaluate the integral. -

Evaluate the improper integral or state that it is divergent. -

Choose the one alternative that best completes the statement or answers the question. Evaluate the integral -

Choose the one alternative that best completes the statement or answers the question. Evaluate the integral -

Evaluate the integral. -

Evaluate the improper integral or state that it is divergent. -

Choose the one alternative that best completes the statement or answers the question. Evaluate the integral -

Integrate the function. - dy

Determine whether the integral converges or diverges. -

Express the integrand as a sum of partial fractions and evaluate the integral. -

Evaluate the integral. -

Functions

Limits

Derivatives

Applications of the Derivative

Integration

Applications of Integration

Logarithmic, Exponential, and Hyperbolic Functions

Differential Equations

Sequences and Infinite Series

Power Series

Parametric and Polar Curves

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Calculus

Filters

Express the integrand as a sum of partial fractions and evaluate the integral. - $Express the integrand as a sum of partial fractions and evaluate the integral. - dx$ dx

Express the integrand as a sum of partial fractions and evaluate the integral. - $Express the integrand as a sum of partial fractions and evaluate the integral. - dx$ dx

Express the integrand as a sum of partial fractions and evaluate the integral. - $Express the integrand as a sum of partial fractions and evaluate the integral. -$