Question 1

Evaluate the improper integral.
-

Accepted Answer

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

Question 2

Solve the problem by integration.
-The general expression for the slope of a curve is   Find the equation of the curve if it passes through (1, 0).

Accepted Answer

A)  y = ln   
B)  y = ln   
C)  y = ln   
D)  y = ln   
A)  y = ln   
B)  y = ln   
C)  y = ln   
D)  y = ln

Question 3

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

Accepted Answer

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

Question 4

Evaluate the integral.
-

Accepted Answer

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

Question 5

Give the appropriate form of the partial fraction decomposition.
-

Accepted Answer

A)    +   
B)  1 +   +   
C)    +   
D)  1 +   +   
A)    +   
B)  1 +   +   
C)    +   
D)  1 +   +

Question 6

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)  Integrate by parts with u = cos 2x, dv = 3x dx 
B)  Integrate by parts with u = 3x, dv = cos 2x dx 
C)  Substitute, letting u = 2x 
D)  Substitute, letting u = cos 2x 
A)  Integrate by parts with u = cos 2x, dv = 3x dx 
B)  Integrate by parts with u = 3x, dv = cos 2x dx 
C)  Substitute, letting u = 2x 
D)  Substitute, letting u = cos 2x

Question 7

Use Simpson's Rule with n = 4 steps to estimate the integral.
-

Accepted Answer

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

Question 8

Integrate the function.
-

Accepted Answer

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

Question 9

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 10

Solve the problem by integration.
-The force F (in N) applied by a stamping machine in making a certain computer part is   where x is the distance (in cm) through which the force acts. Find the work done by the force from   to

Accepted Answer

A)  0.0013 N. cm 
B)  12.2417 N. cm 
C)  0.0066 N. cm 
D)  0.0632 N. cm 
A)  0.0013 N. cm 
B)  12.2417 N. cm 
C)  0.0066 N. cm 
D)  0.0632 N. cm

Question 11

Evaluate the integral.
-    dx

Accepted Answer

A)    
B)  41,984 
C)  15,136 
D)    
A)    
B)  41,984 
C)  15,136 
D)

Question 12

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 13

Evaluate the integral.
-

Accepted Answer

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

Question 14

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)  24.84 
B)  42.69 
C)  30.48 
D)  34.93 
A)  24.84 
B)  42.69 
C)  30.48 
D)  34.93

Question 15

Solve the problem.
-Find the volume of the solid generated by revolving the region in the first quadrant bounded by   and the   from   to   about the

Accepted Answer

A)  14$\pi$ln 7 
B)  2$\pi$( 7ln 7 - 7) 
C)  2$\pi$( 7ln 7 - 6) 
D)  7$\pi$ln 7 
A)  14$\pi$ln 7 
B)  2$\pi$( 7ln 7 - 7) 
C)  2$\pi$( 7ln 7 - 6) 
D)  7$\pi$ln 7

Question 16

Solve the problem.
-Find the volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve y =   , and the line x = 3 about the y-axis.

Accepted Answer

A)    $\pi$ (1 - 11    ) 
B)    $\pi$ (1 - 12    ) 
C)  -   $\pi$(1 + 13   ) 
D)    $\pi$(1 - 13   ) 
A)    $\pi$ (1 - 11    ) 
B)    $\pi$ (1 - 12    ) 
C)  -   $\pi$(1 + 13   ) 
D)    $\pi$(1 - 13   )

Question 17

Solve the problem.
-Find the volume of the solid generated by revolving the region in the first quadrant bounded by the x-axis and the curve y = sin 3x, 0 $\le$ x$\le$  $\pi$/ 3 about the line x = $\pi$/ 3.

Accepted Answer

A)    
B)    $\pi$ 
C)      
D)      - $\pi$ 
A)    
B)    $\pi$ 
C)      
D)      - $\pi$

Question 18

Evaluate the integral by using a substitution prior to integration by parts.
-

Accepted Answer

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

Question 19

Evaluate the integral.
-

Accepted Answer

A)    
B)  1 
C)    
D)  Diverges 
A)    
B)  1 
C)    
D)  Diverges

Question 20

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

Accepted Answer

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

Evaluate the improper integral. -

Solve the problem by integration. -The general expression for the slope of a curve is Find the equation of the curve if it passes through (1, 0).

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

Evaluate the integral. -

Give the appropriate form of the partial fraction decomposition. - $Give the appropriate form of the partial fraction decomposition. -$

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. -

Use Simpson's Rule with n = 4 steps to estimate the integral. -

Integrate the function. -

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

Solve the problem by integration. -The force F (in N) applied by a stamping machine in making a certain computer part is where x is the distance (in cm) through which the force acts. Find the work done by the force from to

Evaluate the integral. - 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

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.

Solve the problem. -Find the volume of the solid generated by revolving the region in the first quadrant bounded by and the from to about the

Solve the problem. -Find the volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve y = , and the line x = 3 about the y-axis.

Solve the problem. -Find the volume of the solid generated by revolving the region in the first quadrant bounded by the x-axis and the curve y = sin 3x, 0 $\le$ x $\le$ $\pi$ / 3 about the line x = $\pi$ / 3.

Evaluate the integral by using a substitution prior to integration by parts. -

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

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. -

Solve the problem by integration. -The general expression for the slope of a curve is Find the equation of the curve if it passes through (1, 0).

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

Evaluate the integral. -

Give the appropriate form of the partial fraction decomposition. -

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. -

Use Simpson's Rule with n = 4 steps to estimate the integral. -

Integrate the function. -

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

Solve the problem by integration. -The force F (in N) applied by a stamping machine in making a certain computer part is where x is the distance (in cm) through which the force acts. Find the work done by the force from to

Evaluate the integral. - dx

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

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.

Solve the problem. -Find the volume of the solid generated by revolving the region in the first quadrant bounded by and the from to about the

Solve the problem. -Find the volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve y = , and the line x = 3 about the y-axis.

Solve the problem. -Find the volume of the solid generated by revolving the region in the first quadrant bounded by the x-axis and the curve y = sin 3x, 0 ≤\le≤ x ≤\le≤ π\piπ / 3 about the line x = π\piπ / 3.

Evaluate the integral by using a substitution prior to integration by parts. -

Evaluate the integral. -

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

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

Give the appropriate form of the partial fraction decomposition. - $Give the appropriate form of the partial fraction decomposition. -$

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

Solve the problem. -Find the volume of the solid generated by revolving the region in the first quadrant bounded by the x-axis and the curve y = sin 3x, 0 $\le$ x $\le$ $\pi$ / 3 about the line x = $\pi$ / 3.

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