Question 1

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

Accepted Answer

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

Question 2

Solve the problem.
-Find the volume of the solid generated by revolving the region in the first quadrant bounded by the x-axis and the curve y = x cos x, 0$\le$x $\le$  $\pi$/2 about the y-axis.

Accepted Answer

A)    - 8  $\pi$ 
B)    - 4 $\pi$ 
C)    + 2   - 4  $\pi$ 
D)    - 4  $\pi$ 
A)    - 8  $\pi$ 
B)    - 4 $\pi$ 
C)    + 2   - 4  $\pi$ 
D)    - 4  $\pi$

Question 3

Evaluate the integral.
-

Accepted Answer

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

Question 4

Evaluate the integral.
-

Accepted Answer

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

Question 5

Evaluate the integral.
-

Accepted Answer

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

Question 6

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

Accepted Answer

A)  tan$\theta$ + sec $\theta$ 
B)    $\theta$ - tan $\theta$ 
C)  tan $\theta$ - sec $\theta$ 
D)   $\theta$ + sec $\theta$ 
A)  tan$\theta$ + sec $\theta$ 
B)    $\theta$ - tan $\theta$ 
C)  tan $\theta$ - sec $\theta$ 
D)   $\theta$ + sec $\theta$

Question 7

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 8

Evaluate the integral.
-

Accepted Answer

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

Question 9

Solve the problem.
-Suppose that the accompanying table shows the velocity of a car every second for 8 seconds. Use the Trapezoidal Rule to approximate the distance traveled by the car in the 8 seconds. Round your answer to the nearest tenth if necessary.

Accepted Answer

A)  307 ft 
B)  171 ft 
C)  233.5 ft 
D)  153.5 ft 
A)  307 ft 
B)  171 ft 
C)  233.5 ft 
D)  153.5 ft

Question 10

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

Accepted Answer

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

Question 11

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

Accepted Answer

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

Question 12

Find the volume.
-Find the volume of the solid generated by revolving the region in the first quadrant under the curve   bounded on the left by x = 1, about the x-axis.

Accepted Answer

A)  100$\pi$ 
B)  2$\pi$ 
C)  10$\pi$ 
D)    $\pi$ 
A)  100$\pi$ 
B)  2$\pi$ 
C)  10$\pi$ 
D)    $\pi$

Question 13

Solve the problem.
-Find the area of the region bounded by the curves y =   , y =   , and x = 0. Round to 3 decimal places.

Accepted Answer

A)      $\approx$ 2.264 
B)      $\approx$ 2.493 
C)      $\approx$ 2.122 
D)      $\approx$ 2.351 
A)      $\approx$ 2.264 
B)      $\approx$ 2.493 
C)      $\approx$ 2.122 
D)      $\approx$ 2.351

Question 14

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

Accepted Answer

A)    
B)  -   
C)  0 
D)  Divergent 
A)    
B)  -   
C)  0 
D)  Divergent

Question 15

Use reduction formulas to 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

Use reduction formulas to evaluate the integral.
-

Accepted Answer

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

Question 18

Use a CAS to perform the integration.
-

Accepted Answer

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

Question 19

Evaluate the integral.
-

Accepted Answer

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

Question 20

Evaluate the integral.
-  (Give your answer in exact form.)

Accepted Answer

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

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

Solve the problem. -Find the volume of the solid generated by revolving the region in the first quadrant bounded by the x-axis and the curve y = x cos x, 0 $\le$ x $\le$ $\pi$ /2 about the y-axis.

Evaluate the integral. -

Evaluate the integral. -

Evaluate the integral. -

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

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

Evaluate the integral. -

Solve the problem. -Suppose that the accompanying table shows the velocity of a car every second for 8 seconds. Use the Trapezoidal Rule to approximate the distance traveled by the car in the 8 seconds. Round your answer to the nearest tenth if necessary.

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

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

Find the volume. -Find the volume of the solid generated by revolving the region in the first quadrant under the curve bounded on the left by x = 1, about the x-axis.

Solve the problem. -Find the area of the region bounded by the curves y = , y = , and x = 0. Round to 3 decimal places.

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

Use reduction formulas to evaluate the integral. -

Evaluate the integral. -

Use reduction formulas to evaluate the integral. -

Use a CAS to perform the integration. -

Evaluate the integral. -

Evaluate the integral. - (Give your answer in exact form.)

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

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

Solve the problem. -Find the volume of the solid generated by revolving the region in the first quadrant bounded by the x-axis and the curve y = x cos x, 0 ≤\le≤ x ≤\le≤ π\piπ /2 about the y-axis.

Evaluate the integral. -

Evaluate the integral. -

Evaluate the integral. -

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

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

Evaluate the integral. -

Solve the problem. -Suppose that the accompanying table shows the velocity of a car every second for 8 seconds. Use the Trapezoidal Rule to approximate the distance traveled by the car in the 8 seconds. Round your answer to the nearest tenth if necessary.

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

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

Find the volume. -Find the volume of the solid generated by revolving the region in the first quadrant under the curve bounded on the left by x = 1, about the x-axis.

Solve the problem. -Find the area of the region bounded by the curves y = , y = , and x = 0. Round to 3 decimal places.

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

Use reduction formulas to evaluate the integral. -

Evaluate the integral. -

Use reduction formulas to evaluate the integral. -

Use a CAS to perform the integration. -

Evaluate the integral. -

Evaluate the integral. - (Give your answer in exact form.)

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

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

Solve the problem. -Find the volume of the solid generated by revolving the region in the first quadrant bounded by the x-axis and the curve y = x cos x, 0 $\le$ x $\le$ $\pi$ /2 about the y-axis.

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