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

Evaluate the integral.
-

Accepted Answer

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

Question 3

Give the appropriate form of the partial fraction decomposition.
-

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

Evaluate the integral.
-dt

Accepted Answer

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

Question 12

Integrate the function.
-  dx

Accepted Answer

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

Question 15

Integrate the function.
-  dx, x < 8

Accepted Answer

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

Question 17

Evaluate the integral.
-

Accepted Answer

A)   
B)   
C)   
D)   
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)    
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 
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)    
A)    
B)    
C)  6 
D)

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

Evaluate the integral. -

Give the appropriate form of the partial fraction decomposition. - $Give the appropriate form of the partial fraction decomposition. -$

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. - $Give the appropriate form of the partial fraction decomposition. -$

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

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. -

Evaluate the integral. -

Give the appropriate form of the partial fraction decomposition. -

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. -

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. - 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.

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

Give the appropriate form of the partial fraction decomposition. - $Give the appropriate form of the partial fraction decomposition. -$

Give the appropriate form of the partial fraction decomposition. - $Give the appropriate form of the partial fraction decomposition. -$

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