Question 1

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

Accepted Answer

A)  
B)   
C)  
D)

Question 2

Evaluate the integral.
-

Accepted Answer

A)  
B)  
C)  
D)

Question 3

Give the appropriate form of the partial fraction decomposition.
-

Accepted Answer

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

Question 4

Find the area or volume.
-Find the area of the region in the first quadrant between the curve y =  and the x-axis.

Accepted Answer

A)  3 
B)  1 
C)   
D)   e

Question 5

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

Accepted Answer

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

Question 6

Give the appropriate form of the partial fraction decomposition.
-

Accepted Answer

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

Question 7

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

Accepted Answer

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

Question 8

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

Accepted Answer

A)    
B)    
C)    
D)

Question 9

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

Accepted Answer

A)    
B)     
C)     
D)

Question 10

Evaluate the integral.
-dt

Accepted Answer

A)   
B)  
C)   
D)

Question 11

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

Accepted Answer

A)  -16 
B)  - 8 
C)  0 
D)  8

Question 12

Integrate the function.
- dx

Accepted Answer

A)   
B)   
C)  
D)

Question 13

Evaluate the integral.
-

Accepted Answer

A)  13 sin x - x cos x + C 
B)  13 sin x + 13x cos x + C 
C)  13 sin x - 13 cos x + C 
D)  13 sin x - 13x cos x + C

Question 14

Evaluate the integral.
- 3x dx

Accepted Answer

A)  
B)   
C)   
D)

Question 15

Integrate the function.
- dx, x < 8

Accepted Answer

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

Question 16

Solve the problem.
-The height of a vase is 5 inches. The table shows the circumference of the vase (in inches) at half-inch intervals starting from the top down. Estimate the volume of the vase by using the Trapezoidal rule with n = 10. Round your answer to the nearest thousandth. [Hint: you will first need to find the areas of the cross-sections that correspond to the given circumferences.]

Accepted Answer

A)  61.856  
B)  62.876  
C)  101.552  
D)  105.479

Question 17

Evaluate the integral.
-

Accepted Answer

A)  
B)  
C)  
D)

Question 18

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

Accepted Answer

A)  
B)  
C)  
D)

Question 19

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

Accepted Answer

A)  -6 sin  + C 
B)  -  cos  + C 
C)  6 cos  + C 
D)   sin  + C

Question 20

Find the area or volume.
-Find the area under the curve y =  bounded on the left by x = 8.

Accepted Answer

A)   
B)   
C)  6 
D)

Exam 8: Integration Techniques

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

Evaluate the integral. -

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

Find the area or volume. -Find the area of the region in the first quadrant between the curve y = and the x-axis.

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

Give the appropriate form of the partial fraction decomposition. - $Give the appropriate form of the partial fraction decomposition. - A) 1 + + + B) 1 + + C) 1 + + + D) 1 + + +$

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

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

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

Evaluate the integral. -dt

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

Integrate the function. - dx

Evaluate the integral. -

Evaluate the integral. - 3x dx

Integrate the function. - dx, x < 8

Evaluate the integral. -

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

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

Find the area or volume. -Find the area under the curve y = bounded on the left by x = 8.