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

Question 2

Evaluate the integral.
-

Accepted Answer

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

Question 5

Use reduction formulas to evaluate the integral.
-

Accepted Answer

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

Question 16

Evaluate the integral.
-

Accepted Answer

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

Question 19

Evaluate the integral.
-  dt

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)  -

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

Evaluate the integral. -

Use integration by parts to establish a reduction formula for the integral. - $Use integration by parts to establish a reduction formula for the integral. - , n \neq 1$ , 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 = $Find the area or volume. -Find the area between the graph of y = and the x-axis, for - \infty < x \le 0.$ 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)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. -

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

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. -

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

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

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

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