Question 1

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 the Trapezoidal 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)  9233 gal 
B)  9225 gal 
C)  8383 gal 
D)  10,475 gal

Question 2

Give the appropriate form of the partial fraction decomposition.
-

Accepted Answer

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

Question 3

Solve the problem by integration.
-Find the first-quadrant area bounded by   and

Accepted Answer

A)   ln  
B)   ln  
C)  6 ln  
D)   ln

Question 4

Solve the problem.
-The voltage v (in volts) induced in a tape head is given by  where t is the time (in seconds). Find the average value of v over the interval from t = 0 to t = 4. Round to the nearest volt.

Accepted Answer

A)  183,853 volts 
B)  2,559,851 volts 
C)  28,130 volts 
D)  30 volts

Question 5

Determine whether the integral converges or diverges.
-

Accepted Answer

A)   
B)  
C)  
D)

Question 6

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

Accepted Answer

A)  16  
B)  16$\pi$ 
C)  8  
D)  8

Question 7

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

Accepted Answer

A)   
B)   
C)    
D)

Question 8

Evaluate the integral.
-

Accepted Answer

A)  2  
B)   
C)  2 
D)

Question 9

Evaluate the integral.
-

Accepted Answer

A)    
B)    
C)    
D)

Question 10

Evaluate the integral.
-

Accepted Answer

A)    
B)    
C)    
D)

Question 11

Find the area or volume.
-Find the area of the region bounded by the curve y = 10  , the x-axis, and on the left by x = 1.

Accepted Answer

A)  20 
B)  10 
C)  5 
D)  100

Question 12

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

Accepted Answer

A)  
B)  
C)  
D)

Question 13

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

Accepted Answer

A)  x + 8 ln  + C 
B)  x - 8 ln  + C 
C)  x - 8 ln  + C 
D)   x + 8 ln  + C

Question 14

Evaluate the integral.
-  dx

Accepted Answer

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

Question 15

Evaluate the improper integral.
-

Accepted Answer

A)  8 ln 12 - 4 
B)  8 ln 12 - 8 
C)  8 ln 3 - 4 
D)  -  ln 12 + 4

Question 16

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

Accepted Answer

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

Question 17

Evaluate the integral.
-dx

Accepted Answer

A)   
B)   
C)  
D)

Question 18

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

Accepted Answer

A)   
B)   
C)   
D)  11

Question 19

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

Accepted Answer

A)  
B)  
C)  
D)

Question 20

Solve the problem.
-Estimate the area of the surface generated by revolving the curve 
y = 2  , 0 $\le$ x $\le$3 
about the x-axis. Use Simpson's Rule with n = 6.

Accepted Answer

A)  1007.254 
B)  996.028 
C)  1024.885 
D)  1021.107

Exam 8: Integration Techniques

Give the appropriate form of the partial fraction decomposition. - $Give the appropriate form of the partial fraction decomposition. - A) + B) + C) + D) +$

Solve the problem by integration. -Find the first-quadrant area bounded by and

Solve the problem. -The voltage v (in volts) induced in a tape head is given by where t is the time (in seconds) . Find the average value of v over the interval from t = 0 to t = 4. Round to the nearest volt.

Determine whether the integral converges or diverges. -

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

Evaluate the integral. -

Evaluate the integral. -

Evaluate the integral. -

Find the area or volume. -Find the area of the region bounded by the curve y = 10 , the x-axis, and on the left by x = 1.

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

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

Evaluate the integral. - dx

Evaluate the improper integral. -

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

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. - $Express the integrand as a sum of partial fractions and evaluate the integral. - A) B) C) D)$

Exam 8: Integration Techniques

Give the appropriate form of the partial fraction decomposition. -

Solve the problem by integration. -Find the first-quadrant area bounded by and

Solve the problem. -The voltage v (in volts) induced in a tape head is given by where t is the time (in seconds) . Find the average value of v over the interval from t = 0 to t = 4. Round to the nearest volt.

Determine whether the integral converges or diverges. -

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

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

Evaluate the integral. -

Evaluate the integral. -

Evaluate the integral. -

Find the area or volume. -Find the area of the region bounded by the curve y = 10 , the x-axis, and on the left by x = 1.

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

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

Evaluate the integral. - dx

Evaluate the improper integral. -

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

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. -

Solve the problem. -Estimate the area of the surface generated by revolving the curve y = 2 , 0 ≤\le≤ x ≤\le≤ 3 about the x-axis. Use Simpson's Rule with n = 6.

Give the appropriate form of the partial fraction decomposition. - $Give the appropriate form of the partial fraction decomposition. - A) + B) + C) + D) +$

Express the integrand as a sum of partial fractions and evaluate the integral. - $Express the integrand as a sum of partial fractions and evaluate the integral. - A) B) C) D)$