Question 1

Solve the problem by integration.
-Find the volume generated by rotating the area bounded by       and   about the

Accepted Answer

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

Question 2

Evaluate the integral.
-  Give your answer in exact form.

Accepted Answer

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

Question 3

Solve the problem.
-The following table shows the rate of water flow (in gal/min) from a stream into a pond during a 30-minute period after a thunderstorm. Use Simpson's Rule to estimate the total amount of water flowing into the pond during this period. Round your answer to the nearest gallon.

Accepted Answer

A)  9725 gal 
B)  8475 gal 
C)  7717 gal 
D)  8483 gal 
A)  9725 gal 
B)  8475 gal 
C)  7717 gal 
D)  8483 gal

Question 4

Solve the problem.
-Find the volume of the solid obtained by revolving the region bounded by the curve y =   on   about the y-axis. Round to 3 decimal places.

Accepted Answer

A) $\pi$     $\approx$ 8.268 
B)  $\pi$  $\approx$ 13.497 
C)  $\pi$   $\approx$12.021 
D)  $\pi$   $\approx$ 7.718 
A) $\pi$     $\approx$ 8.268 
B)  $\pi$  $\approx$ 13.497 
C)  $\pi$   $\approx$12.021 
D)  $\pi$   $\approx$ 7.718

Question 5

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

Accepted Answer

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

Question 6

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 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

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

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 9

Find the volume.
-Find the volume of the solid generated by revolving the region under the curve   from   to   about the

Accepted Answer

A)  9$\pi$ 
B)  $\pi$   
C)  18$\pi$ 
D)  9 
A)  9$\pi$ 
B)  $\pi$   
C)  18$\pi$ 
D)  9

Question 10

Evaluate the improper integral.
-

Accepted Answer

A)  -16 
B)  4 
C)  16 
D)  -4 
A)  -16 
B)  4 
C)  16 
D)  -4

Question 11

Evaluate the integral.
-

Accepted Answer

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

Question 12

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

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 13

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

Accepted Answer

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

Question 14

Integrate the function.
-  , x > 7

Accepted Answer

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

Question 15

Solve the problem.
-Consider the region R bounded by the graph of f(x) =   on the interval [0, 3]. Find the volume of the solid formed when R is revolved about the y-axis.

Accepted Answer

A)   $\pi$  
B)  2$\pi$   
C) $\pi$   
D)  2$\pi$  
A)   $\pi$  
B)  2$\pi$   
C) $\pi$   
D)  2$\pi$

Question 16

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

Accepted Answer

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

Question 17

Evaluate the integral.
-

Accepted Answer

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

Question 18

Use reduction formulas to evaluate the integral.
-

Accepted Answer

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

Question 19

Give the appropriate form of the partial fraction decomposition.
-

Accepted Answer

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

Question 20

Evaluate the integral.
-     cos 8$\theta$ d$\theta$

Accepted Answer

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

Solve the problem by integration. -Find the volume generated by rotating the area bounded by and about the

Evaluate the integral. - Give your answer in exact form.

Solve the problem. -The following table shows the rate of water flow (in gal/min) from a stream into a pond during a 30-minute period after a thunderstorm. Use Simpson's Rule to estimate the total amount of water flowing into the pond during this period. Round your answer to the nearest gallon.

Solve the problem. -Find the volume of the solid obtained by revolving the region bounded by the curve y = on about the y-axis. Round to 3 decimal places.

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

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

Use Simpson's Rule with n = 4 steps to estimate 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

Find the volume. -Find the volume of the solid generated by revolving the region under the curve from to about the

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. -

Integrate the function. - , x > 7

Solve the problem. -Consider the region R bounded by the graph of f(x) = on the interval [0, 3]. Find the volume of the solid formed when R is revolved about the y-axis.

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

Evaluate the integral. -

Use reduction formulas to evaluate the integral. -

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

Evaluate the integral. - $Evaluate the integral. - cos 8 \theta d \theta$ cos 8 $\theta$ d $\theta$

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

Solve the problem by integration. -Find the volume generated by rotating the area bounded by and about the

Evaluate the integral. - Give your answer in exact form.

Solve the problem. -The following table shows the rate of water flow (in gal/min) from a stream into a pond during a 30-minute period after a thunderstorm. Use Simpson's Rule to estimate the total amount of water flowing into the pond during this period. Round your answer to the nearest gallon.

Solve the problem. -Find the volume of the solid obtained by revolving the region bounded by the curve y = on about the y-axis. Round to 3 decimal places.

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

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

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

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

Find the volume. -Find the volume of the solid generated by revolving the region under the curve from to about the

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. -

Integrate the function. - , x > 7

Solve the problem. -Consider the region R bounded by the graph of f(x) = on the interval [0, 3]. Find the volume of the solid formed when R is revolved about the y-axis.

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

Evaluate the integral. -

Use reduction formulas to evaluate the integral. -

Give the appropriate form of the partial fraction decomposition. -

Evaluate the integral. - cos 8 θ\thetaθ d θ\thetaθ

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

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

Evaluate the integral. - $Evaluate the integral. - cos 8 \theta d \theta$ cos 8 $\theta$ d $\theta$