Question 1

Evaluate the integral.
-

Accepted Answer

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

Question 2

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

Accepted Answer

A)  49 
B)    
C)    
D)    
A)  49 
B)    
C)    
D)

Question 3

Give the appropriate form of the partial fraction decomposition.
-

Accepted Answer

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

Question 4

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

Accepted Answer

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

Question 5

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

Accepted Answer

A)  1.43 
B)  3.52 
C)  1.76 
D)  0.88 
A)  1.43 
B)  3.52 
C)  1.76 
D)  0.88

Question 6

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 = ln 6 about the line x = ln 6.

Accepted Answer

A)  2$\pi$( 5 + ln 6) 
B)  2$\pi$( 5 - ln 6) 
C)  2$\pi$( 6 - ln 6) 
D)  2$\pi$(6 - ln 7) 
A)  2$\pi$( 5 + ln 6) 
B)  2$\pi$( 5 - ln 6) 
C)  2$\pi$( 6 - ln 6) 
D)  2$\pi$(6 - ln 7)

Question 7

Solve the problem.
-A data-recording thermometer recorded the soil temperature in a field every 2 hours from noon to midnight, as shown in the following table. Use the Trapezoidal Rule to estimate the average temperature for the 12-hour period. Round your answer to the nearest hundredth if necessary.

Accepted Answer

A)  63.94°F 
B)  74.33°F 
C)  76.7°F 
D)  63.92°F 
A)  63.94°F 
B)  74.33°F 
C)  76.7°F 
D)  63.92°F

Question 8

Solve the problem.
-A surveyor measured the length of a piece of land at 100-ft intervals (x), as shown in the table. Use Simpson's Rule to estimate the area of the piece of land in square feet.

Accepted Answer

A)  20,000   
B)  21,000   
C)  20,500   
D)  24,500   
A)  20,000   
B)  21,000   
C)  20,500   
D)  24,500

Question 9

Evaluate the integral.
-

Accepted Answer

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

Question 10

Evaluate the improper integral.
-

Accepted Answer

A)  3 
B)  6 
C)  2 
D)  4 
A)  3 
B)  6 
C)  2 
D)  4

Question 11

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

Accepted Answer

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

Question 12

Give the appropriate form of the partial fraction decomposition.
-

Accepted Answer

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

Question 13

Solve the problem.
-Find the length of the curve y = ln(sin x),  $\pi$/ 6 $\le$ x $\le$  $\pi$/2

Accepted Answer

A)  ln(   + 2) 
B)  ln(   ) 
C)  1 - ln(   + 2) 
D)  ln(   + 1) 
A)  ln(   + 2) 
B)  ln(   ) 
C)  1 - ln(   + 2) 
D)  ln(   + 1)

Question 14

Evaluate the integral.
-

Accepted Answer

A)  4 
B)  2 
C)  1 
D)  0 
A)  4 
B)  2 
C)  1 
D)  0

Question 15

Solve the problem.
-Find the length of the curve y = ln(csc x), $\pi$/ 3 $\le$ x $\le$ $\pi$/2

Accepted Answer

A)  ln(   + 1) 
B)  ln(   ) 
C)  ln( 2   ) 
D)  1 - ln(   ) 
A)  ln(   + 1) 
B)  ln(   ) 
C)  ln( 2   ) 
D)  1 - ln(   )

Question 16

Solve the problem.
-Find the volume of the solid generated by revolving the region bounded by the curve   the   and the vertical line   about the x-axis.

Accepted Answer

A) $\pi$e - 1) 
B)  2$\pi$(   - 1) 
C)  $\pi$ e 
D)  $\pi$(   - 1) 
A) $\pi$e - 1) 
B)  2$\pi$(   - 1) 
C)  $\pi$ e 
D)  $\pi$(   - 1)

Question 17

Solve the problem.
-Find the area bounded by y =   , x = 0, y = 0, and x = 2.

Accepted Answer

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

Question 18

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

Accepted Answer

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

Question 19

Solve the problem.
-Find the volume generated by revolving the curve y = cos 4x about the x-axis, 0 $\le$ x $\le$  $\pi$/ 48

Accepted Answer

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

Question 20

Evaluate the integral.
-

Accepted Answer

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

Evaluate the integral. -

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

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

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

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 = ln 6 about the line x = ln 6.

Solve the problem. -A surveyor measured the length of a piece of land at 100-ft intervals (x), as shown in the table. Use Simpson's Rule to estimate the area of the piece of land in square feet.

Evaluate the integral. -

Evaluate the improper integral. -

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

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

Solve the problem. -Find the length of the curve y = ln(sin x), $\pi$ / 6 $\le$ x $\le$ $\pi$ /2

Evaluate the integral. -

Solve the problem. -Find the length of the curve y = ln(csc x), $\pi$ / 3 $\le$ x $\le$ $\pi$ /2

Solve the problem. -Find the volume of the solid generated by revolving the region bounded by the curve the and the vertical line about the x-axis.

Solve the problem. -Find the area bounded by y = , x = 0, y = 0, and x = 2.

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

Solve the problem. -Find the volume generated by revolving the curve y = cos 4x about the x-axis, 0 $\le$ x $\le$ $\pi$ / 48

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

Evaluate the integral. -

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

Give the appropriate form of the partial fraction decomposition. -

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. -

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 = ln 6 about the line x = ln 6.

Solve the problem. -A surveyor measured the length of a piece of land at 100-ft intervals (x), as shown in the table. Use Simpson's Rule to estimate the area of the piece of land in square feet.

Evaluate the integral. -

Evaluate the improper integral. -

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

Give the appropriate form of the partial fraction decomposition. -

Solve the problem. -Find the length of the curve y = ln(sin x), π\piπ / 6 ≤\le≤ x ≤\le≤ π\piπ /2

Evaluate the integral. -

Solve the problem. -Find the length of the curve y = ln(csc x), π\piπ / 3 ≤\le≤ x ≤\le≤ π\piπ /2

Solve the problem. -Find the volume of the solid generated by revolving the region bounded by the curve the and the vertical line about the x-axis.

Solve the problem. -Find the area bounded by y = , x = 0, y = 0, and x = 2.

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

Solve the problem. -Find the volume generated by revolving the curve y = cos 4x about the x-axis, 0 ≤\le≤ x ≤\le≤ π\piπ / 48

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

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

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

Solve the problem. -Find the length of the curve y = ln(sin x), $\pi$ / 6 $\le$ x $\le$ $\pi$ /2

Solve the problem. -Find the length of the curve y = ln(csc x), $\pi$ / 3 $\le$ x $\le$ $\pi$ /2

Solve the problem. -Find the volume generated by revolving the curve y = cos 4x about the x-axis, 0 $\le$ x $\le$ $\pi$ / 48