Question 1

Solve the problem by integration.
-Find the volume generated by revolving the first-quadrant area bounded by  and  about the

Accepted Answer

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

Question 2

Evaluate the integral.
-

Accepted Answer

A)    
B)    
C)   
D)

Question 3

Find the surface area or volume.
-The region between the curve y =  , -0.4 $\le$ x $\le$ 0.4, and the x-axis is revolved about the x-axis to generate a solid. Use a table of integrals to find the volume of the solid generated to two decimal places.

Accepted Answer

A)  1.50 
B)  1.62 
C)  1.27 
D)  1.34

Question 4

Use integration by parts to establish a reduction formula for the integral.
- , n $\neq$1

Accepted Answer

A)    
B)     
C)     
D)

Question 5

Use reduction formulas to evaluate the integral.
-

Accepted Answer

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

Question 6

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

Accepted Answer

A)  
B)  
C)  
D)

Question 7

Find the area or volume.
-Find the area between the graph of y =  and the x-axis, for -$\infty$ < x $\le$ 0.

Accepted Answer

A)  14 
B)  1 
C)  7 
D)

Question 8

Find the surface area or volume.
-Use substitution and a table of integrals to find, to two decimal places, the area of the surface generated by revolving the curve   about the x-axis.

Accepted Answer

A)  83,719.65 
B)  90,329.45 
C)  69,213.13 
D)  74,906.59

Question 9

Evaluate the integral.
-

Accepted Answer

A)  
B)  
C)  
D)

Question 10

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

Accepted Answer

A)  -  ln 11 
B)   ln 6 
C)   ln  
D)   ln 11

Question 11

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

Accepted Answer

A)   
B)  0 
C)   
D)  $\pi$ + 9

Question 12

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

Accepted Answer

A)   
B)   
C)   
D)

Question 13

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 14

Solve the problem.
-The charge q (in coulombs) delivered by a current i (in amperes) is given by  where t is the time (in seconds). A damped-out periodic wave form has current given by  Find a formula for the charge delivered over time t.

Accepted Answer

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

Question 15

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

Accepted Answer

A)     
B)     
C)   
D)

Question 16

Evaluate the integral.
-

Accepted Answer

A)  
B)  
C)  
D)

Question 17

Solve the problem.
-Find the area between y = (x - 2)ex and the x-axis from x = 2 to x = 6.

Accepted Answer

A)  e6 + e2  
B)  3e6  
C)  3e6 + e2  
D)  e6 - e2

Question 18

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

Accepted Answer

A)  Divergent 
B)  - 1 
C)   
D)

Question 19

Evaluate the integral.
- dt

Accepted Answer

A)  
B)  
C)  
D)

Question 20

Evaluate the integral.
-

Accepted Answer

A)   
B)   
C)   
D)  -

Exam 8: Integration Techniques

Evaluate the integral. -

Use integration by parts to establish a reduction formula for the integral. - $Use integration by parts to establish a reduction formula for the integral. - , n \neq 1 A) B) C) D)$ , n $\neq$ 1

Use reduction formulas to evaluate the integral. -

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

Find the area or volume. -Find the area between the graph of y = $Find the area or volume. -Find the area between the graph of y = and the x-axis, for - \infty < x \le 0. A) 14 B) 1 C) 7 D)$ and the x-axis, for - $\infty$ < x $\le$ 0.

Find the surface area or volume. -Use substitution and a table of integrals to find, to two decimal places, the area of the surface generated by revolving the curve about the x-axis.

Evaluate the integral. -

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

Evaluate the improper integral or state that it is divergent. - $Evaluate the improper integral or state that it is divergent. - A) B) 0 C) D) \pi + 9$

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 -

Solve the problem. -The charge q (in coulombs) delivered by a current i (in amperes) is given by where t is the time (in seconds) . A damped-out periodic wave form has current given by Find a formula for the charge delivered over time t.

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

Evaluate the integral. -

Solve the problem. -Find the area between y = (x - 2) e^x and the x-axis from x = 2 to x = 6.

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

Evaluate the integral. - dt

Evaluate the integral. -

Exam 8: Integration Techniques

Solve the problem by integration. -Find the volume generated by revolving the first-quadrant area bounded by and about the

Evaluate the integral. -

Find the surface area or volume. -The region between the curve y = , -0.4 ≤\le≤ x ≤\le≤ 0.4, and the x-axis is revolved about the x-axis to generate a solid. Use a table of integrals to find the volume of the solid generated to two decimal places.

Use integration by parts to establish a reduction formula for the integral. - , n ≠\neq= 1

Use reduction formulas to evaluate the integral. -

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

Find the area or volume. -Find the area between the graph of y = and the x-axis, for - ∞\infty∞ < x ≤\le≤ 0.

Find the surface area or volume. -Use substitution and a table of integrals to find, to two decimal places, the area of the surface generated by revolving the curve about the x-axis.

Evaluate the integral. -

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

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

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 -

Solve the problem. -The charge q (in coulombs) delivered by a current i (in amperes) is given by where t is the time (in seconds) . A damped-out periodic wave form has current given by Find a formula for the charge delivered over time t.

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

Evaluate the integral. -

Solve the problem. -Find the area between y = (x - 2) ex and the x-axis from x = 2 to x = 6.

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

Evaluate the integral. - dt

Evaluate the integral. -

Use integration by parts to establish a reduction formula for the integral. - $Use integration by parts to establish a reduction formula for the integral. - , n \neq 1 A) B) C) D)$ , n $\neq$ 1

Find the area or volume. -Find the area between the graph of y = $Find the area or volume. -Find the area between the graph of y = and the x-axis, for - \infty < x \le 0. A) 14 B) 1 C) 7 D)$ and the x-axis, for - $\infty$ < x $\le$ 0.

Evaluate the improper integral or state that it is divergent. - $Evaluate the improper integral or state that it is divergent. - A) B) 0 C) D) \pi + 9$

Solve the problem. -Find the area between y = (x - 2) e^x and the x-axis from x = 2 to x = 6.