Question 1

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

Accepted Answer

A)  Divergent 
B)  -24 
C)  24 
D)  48 
A)  Divergent 
B)  -24 
C)  24 
D)  48

Question 2

Solve the problem by integration.
-Under specified conditions, the time t (in min) required to form x grams of a substance during a chemical reaction is given by   Find the equation relating t and x if x = 0 g when

Accepted Answer

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

Question 3

Evaluate the integral.
-

Accepted Answer

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

Question 4

Use integration by parts to establish a reduction formula for the integral.
-

Accepted Answer

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

Question 5

Evaluate the integral.
-

Accepted Answer

A)  40.2 
B)  6.70 
C)  55.2 
D)  9.48 
A)  40.2 
B)  6.70 
C)  55.2 
D)  9.48

Question 6

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

Accepted Answer

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

Question 7

Evaluate the integral.
-   dx

Accepted Answer

A)    
B)    
C)  0 
D)  2 
A)    
B)    
C)  0 
D)  2

Question 8

Use integration by parts to establish a reduction formula for the integral.
-

Accepted Answer

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

Question 9

Evaluate the integral.
-

Accepted Answer

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

Question 10

Find the surface area or volume.
-Use an integral table and a calculator to find to two decimal places the area of the surface generated by revolving the curve     about the x-axis.

Accepted Answer

A)  261.32 
B)  372.65 
C)  186.32 
D)  319.41 
A)  261.32 
B)  372.65 
C)  186.32 
D)  319.41

Question 11

Evaluate the integral.
-

Accepted Answer

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

Question 12

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

Accepted Answer

A)  0 
B)  2 
C)  4 
D)  Divergent 
A)  0 
B)  2 
C)  4 
D)  Divergent

Question 13

Determine whether the integral converges or diverges.
-

Accepted Answer

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

Question 14

Evaluate the integral by making a substitution and then using a table of integrals.
-  d  $\theta$

Accepted Answer

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

Question 15

Solve the problem by integration.
-Find the volume generated by revolving the first-quadrant area bounded by   and x = 5 about the y-axis.

Accepted Answer

A)  10 $\pi$ ln   
B)     $\pi$ ln 4536 
C)  5 $\pi$ ln 4536 
D)  5 $\pi$ ln   
A)  10 $\pi$ ln   
B)     $\pi$ ln 4536 
C)  5 $\pi$ ln 4536 
D)  5 $\pi$ ln

Question 16

Integrate the function.
-  , x >

Accepted Answer

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

Question 17

Integrate the function.
-

Accepted Answer

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

Question 18

Evaluate the integral.
-

Accepted Answer

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

Question 19

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 20

Evaluate the improper integral.
-

Accepted Answer

A)    
B)  1 
C)    
D)  18 
A)    
B)  1 
C)    
D)  18

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

Solve the problem by integration. -Under specified conditions, the time t (in min) required to form x grams of a substance during a chemical reaction is given by Find the equation relating t and x if x = 0 g when

Evaluate the integral. -

Use integration by parts to establish a reduction formula for the integral. -

Evaluate the integral. -

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

Evaluate the integral. - dx

Use integration by parts to establish a reduction formula for the integral. -

Evaluate the integral. -

Find the surface area or volume. -Use an integral table and a calculator to find to two decimal places the area of the surface generated by revolving the curve about the x-axis.

Evaluate the integral. -

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

Determine whether the integral converges or diverges. -

Evaluate the integral by making a substitution and then using a table of integrals. - $Evaluate the integral by making a substitution and then using a table of integrals. - d \theta$ d $\theta$

Solve the problem by integration. -Find the volume generated by revolving the first-quadrant area bounded by and x = 5 about the y-axis.

Integrate the function. - , x >

Integrate the function. -

Evaluate the integral. -

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

Evaluate the improper 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

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

Solve the problem by integration. -Under specified conditions, the time t (in min) required to form x grams of a substance during a chemical reaction is given by Find the equation relating t and x if x = 0 g when

Evaluate the integral. -

Use integration by parts to establish a reduction formula for the integral. -

Evaluate the integral. -

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

Evaluate the integral. - dx

Use integration by parts to establish a reduction formula for the integral. -

Evaluate the integral. -

Find the surface area or volume. -Use an integral table and a calculator to find to two decimal places the area of the surface generated by revolving the curve about the x-axis.

Evaluate the integral. -

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

Determine whether the integral converges or diverges. -

Evaluate the integral by making a substitution and then using a table of integrals. - d θ\thetaθ

Solve the problem by integration. -Find the volume generated by revolving the first-quadrant area bounded by and x = 5 about the y-axis.

Integrate the function. - , x >

Integrate the function. -

Evaluate the integral. -

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

Evaluate the improper 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

Evaluate the integral by making a substitution and then using a table of integrals. - $Evaluate the integral by making a substitution and then using a table of integrals. - d \theta$ d $\theta$