Question 1

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

Accepted Answer

A)    
B)  -3$\pi$ 
C)  -   
D)  0 
A)    
B)  -3$\pi$ 
C)  -   
D)  0 C

Question 2

Solve the problem.
-Find the area bounded by y( 49 + 16   ) = 4, x = 0, y = 0, and x = 5.

Accepted Answer

A)        
B)  4     
C)        
D)      
A)        
B)  4     
C)        
D)      C

Question 3

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

Accepted Answer

A)    ln 5 
B)    ln 4 
C)  -   ln 5 
D)  4 ln 5 
A)    ln 5 
B)    ln 4 
C)  -   ln 5 
D)  4 ln 5 A

Question 4

Use a CAS to perform the integration.
-

Accepted Answer

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

Question 5

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

Accepted Answer

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

Question 6

Find the indicated Simpson's Rule approximations to the integral. Round to 5 decimal places.
-  using n = 4 and n = 8 subintervals

Accepted Answer

A)  40.71405 for n = 4; 81.44146 for n = 8 
B)  27.14715 for n = 4; 27.14270 for n = 8 
C)  27.14270 for n = 4; 27.14715 for n = 8 
D)  81.44146 for n = 4; 40.71405 for n = 8 
A)  40.71405 for n = 4; 81.44146 for n = 8 
B)  27.14715 for n = 4; 27.14270 for n = 8 
C)  27.14270 for n = 4; 27.14715 for n = 8 
D)  81.44146 for n = 4; 40.71405 for n = 8

Question 7

Solve the problem.
-The growth rate of a certain tree (in feet) is given by y =   +   , where t is time in years. Estimate the total growth of the tree through the end of the second year by using Simpson's rule. Use 2 subintervals. Round your answer to the nearest hundredth.

Accepted Answer

A)  2.34 ft 
B)  3.68 ft 
C)  5.11 ft 
D)  3.41 ft 
A)  2.34 ft 
B)  3.68 ft 
C)  5.11 ft 
D)  3.41 ft

Question 8

Evaluate the integral.
-

Accepted Answer

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

Question 9

Evaluate the integral.
-

Accepted Answer

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

Question 10

Integrate the function.
-  dx

Accepted Answer

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

Question 11

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

Accepted Answer

A)  1   
B)  144 
C)  2304 
D)  144   
A)  1   
B)  144 
C)  2304 
D)  144

Question 12

Evaluate the integral.
-

Accepted Answer

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

Question 13

Give the appropriate form of the partial fraction decomposition.
-

Accepted Answer

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

Question 14

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

Accepted Answer

A)  -1 - 2   
B)  -   
C)  -   
D)  -   
A)  -1 - 2   
B)  -   
C)  -   
D)  -

Question 15

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

Accepted Answer

A)  ln 1 
B)    
C)  Divergent 
D)  ln 3 
A)  ln 1 
B)    
C)  Divergent 
D)  ln 3

Question 16

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

Accepted Answer

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

Question 17

Evaluate the integral.
-   dx

Accepted Answer

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

Question 18

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

Accepted Answer

A)  56 
B)  28 
C)  112 
D)    
A)  56 
B)  28 
C)  112 
D)

Question 19

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

Accepted Answer

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

Question 20

Evaluate the integral.
-    x dx

Accepted Answer

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

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

Solve the problem. -Find the area bounded by y( 49 + 16 ) = 4, x = 0, y = 0, and x = 5.

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

Use a CAS to perform the integration. -

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

Find the indicated Simpson's Rule approximations to the integral. Round to 5 decimal places. - using n = 4 and n = 8 subintervals

Solve the problem. -The growth rate of a certain tree (in feet) is given by y = + , where t is time in years. Estimate the total growth of the tree through the end of the second year by using Simpson's rule. Use 2 subintervals. Round your answer to the nearest hundredth.

Evaluate the integral. -

Evaluate the integral. -

Integrate the function. - dx

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

Evaluate 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. -

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

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

Evaluate the integral. - dx

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

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

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

Solve the problem. -Find the area bounded by y( 49 + 16 ) = 4, x = 0, y = 0, and x = 5.

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

Use a CAS to perform the integration. -

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

Find the indicated Simpson's Rule approximations to the integral. Round to 5 decimal places. - using n = 4 and n = 8 subintervals

Solve the problem. -The growth rate of a certain tree (in feet) is given by y = + , where t is time in years. Estimate the total growth of the tree through the end of the second year by using Simpson's rule. Use 2 subintervals. Round your answer to the nearest hundredth.

Evaluate the integral. -

Evaluate the integral. -

Integrate the function. - dx

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

Evaluate the integral. -

Give the appropriate form of the partial fraction decomposition. -

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

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

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

Evaluate the integral. - dx

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

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

Evaluate the integral. - x 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. - $Give the appropriate form of the partial fraction decomposition. -$