Question 1

Integrate the function.
-

Accepted Answer

A)      
B)        
C)      
D)  9     
A)      
B)        
C)      
D)  9

Question 2

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

Accepted Answer

A)  Divergent 
B)  0.3333 
C)  -2.3333 
D)  -4.667 
A)  Divergent 
B)  0.3333 
C)  -2.3333 
D)  -4.667

Question 3

Evaluate the integral.
- ln 2x dx

Accepted Answer

A)  51.35 
B)  37.13 
C)  38.91 
D)  -19.37 
A)  51.35 
B)  37.13 
C)  38.91 
D)  -19.37

Question 4

Evaluate the integral.
-

Accepted Answer

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

Question 5

Integrate the function.
-  dt

Accepted Answer

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

Question 6

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 7

Use integration by parts to establish a reduction formula for the integral.
-  , n $\neq$1

Accepted Answer

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

Question 8

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

Accepted Answer

A)  2 
B)  0 
C)  -2 
D)  Divergent 
A)  2 
B)  0 
C)  -2 
D)  Divergent

Question 9

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

Accepted Answer

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

Question 10

Evaluate the integral.
-

Accepted Answer

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

Question 11

Use the Trapezoidal Rule with n = 4 steps to estimate the integral.
-

Accepted Answer

A)  100 
B)  25 
C)  50 
D)    
A)  100 
B)  25 
C)  50 
D)

Question 12

Identify a technique of integration for evaluating the integral. If necessary, explain how to first simplify the integrand before applying the suggested technique of integration. You do not need to evaluate the integral.
-

Accepted Answer

A)  Substitute, letting u =   x 
B)  Integrate by parts with u =   x, dv = (1 - cot x) dx 
C)  Integrate by parts with u = 1-cot x, dv =   x dx 
D)  Substitute, letting u = 1-cot x 
A)  Substitute, letting u =   x 
B)  Integrate by parts with u =   x, dv = (1 - cot x) dx 
C)  Integrate by parts with u = 1-cot x, dv =   x dx 
D)  Substitute, letting u = 1-cot x

Question 13

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

Accepted Answer

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

Question 14

Solve the problem.
-Find the area of the entire region bounded by the curves   and

Accepted Answer

A)  1 
B)    - 6 ln 12 
C)  0 
D)  9 - 12 ln 12 
A)  1 
B)    - 6 ln 12 
C)  0 
D)  9 - 12 ln 12

Question 15

Solve the problem by integration.
-The current i (in A) as a function of the time t (in s) in a certain electric circuit is given by   Find the total charge that passes a given point in the circuit during the first two seconds.

Accepted Answer

A)  3.367 C 
B)  3.332 C 
C)  1.122 C 
D)  10.102 C 
A)  3.367 C 
B)  3.332 C 
C)  1.122 C 
D)  10.102 C

Question 16

Find the volume.
-Find the volume of the solid generated by revolving the area under y = 5   in the first quadrant about the x-axis

Accepted Answer

A)  5$\pi$ 
B)  25$\pi$ 
C)  50$\pi$ 
D)    $\pi$ 
A)  5$\pi$ 
B)  25$\pi$ 
C)  50$\pi$ 
D)    $\pi$

Question 17

Evaluate the improper integral.
-

Accepted Answer

A)  -8 
B)  8 
C)  4 
D)  0 
A)  -8 
B)  8 
C)  4 
D)  0

Question 18

Evaluate the integral.
-

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

Question 20

Use integration by parts to establish a reduction formula for the integral.
-  , n $\neq$1

Accepted Answer

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

Integrate the function. -

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

Evaluate the integral. -ln 2x dx

Evaluate the integral. -

Integrate the function. - dt

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

Use integration by parts to establish a reduction formula for the integral. - $Use integration by parts to establish a reduction formula for the integral. - , n \neq 1$ , n $\neq$ 1

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

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

Evaluate the integral. -

Use the Trapezoidal Rule with n = 4 steps to estimate the integral. -

Identify a technique of integration for evaluating the integral. If necessary, explain how to first simplify the integrand before applying the suggested technique of integration. You do not need to evaluate the integral. -

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

Solve the problem. -Find the area of the entire region bounded by the curves and

Solve the problem by integration. -The current i (in A) as a function of the time t (in s) in a certain electric circuit is given by Find the total charge that passes a given point in the circuit during the first two seconds.

Find the volume. -Find the volume of the solid generated by revolving the area under y = 5 in the first quadrant about the x-axis

Evaluate the improper integral. -

Evaluate the integral. -

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

Use integration by parts to establish a reduction formula for the integral. - $Use integration by parts to establish a reduction formula for the integral. - , n \neq 1$ , n $\neq$ 1

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. -

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

Evaluate the integral. -ln 2x dx

Evaluate the integral. -

Integrate the function. - dt

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

Use integration by parts to establish a reduction formula for the integral. - , n ≠\neq= 1

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

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

Evaluate the integral. -

Use the Trapezoidal Rule with n = 4 steps to estimate the integral. -

Identify a technique of integration for evaluating the integral. If necessary, explain how to first simplify the integrand before applying the suggested technique of integration. You do not need to evaluate the integral. -

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

Solve the problem. -Find the area of the entire region bounded by the curves and

Solve the problem by integration. -The current i (in A) as a function of the time t (in s) in a certain electric circuit is given by Find the total charge that passes a given point in the circuit during the first two seconds.

Find the volume. -Find the volume of the solid generated by revolving the area under y = 5 in the first quadrant about the x-axis

Evaluate the improper integral. -

Evaluate the integral. -

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

Use integration by parts to establish a reduction formula for the integral. - , n ≠\neq= 1

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

Use integration by parts to establish a reduction formula for the integral. - $Use integration by parts to establish a reduction formula for the integral. - , n \neq 1$ , n $\neq$ 1

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

Use integration by parts to establish a reduction formula for the integral. - $Use integration by parts to establish a reduction formula for the integral. - , n \neq 1$ , n $\neq$ 1