Question 1

Find the indefinite integral.

Accepted Answer

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

Question 2

Determine whether the improper integral   diverges or converges. Evaluate the integral if it converges.

Accepted Answer

A)  8 
B)  6 
C)  2 
D)    
E)  diverges 
A)  8 
B)  6 
C)  2 
D)    
E)  diverges

Question 3

Determine whether the improper integral   diverges or converges.

Accepted Answer

A)    
B)    
A)    
B)

Question 4

Use partial fractions to find the integral   .

Accepted Answer

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

Question 5

Determine whether the improper integral   diverges or converges. Evaluate the integral if it converges.

Accepted Answer

A)    
B)    
C)    
D)    
E)  diverges 
A)    
B)    
C)    
D)    
E)  diverges

Question 6

Use partial fractions to find   .

Accepted Answer

A)    (1/       )   
B)    
C)    (1/         
D)    
E)    artcat(   )   
A)    (1/       )   
B)    
C)    (1/         
D)    
E)    artcat(   )

Question 7

Find the indefinite integral by making the substitution   .

Accepted Answer

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

Question 8

Find the indefinite integral.

Accepted Answer

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

Question 9

Determine whether the improper integral   diverges or converges. Evaluate the integral if it converges.

Accepted Answer

A)    
B)    
C)    
D)      
E)  diverges 
A)    
B)    
C)    
D)      
E)  diverges

Question 10

Apply the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral using 16 subintervals. Round your answer to six decimal places and compare the result with the exact value of the definite integral. ​   ​

Accepted Answer

A)  The Trapezoidal rule gives 5.008090 and Simpson's rule gives 5.258495. 
B)  The Trapezoidal rule gives -5.008090 and Simpson's rule gives -5.008382. 
C)  The Trapezoidal rule gives 5.008090 and Simpson's rule gives 5.008382. 
D)  The Trapezoidal rule gives 5.007217 and Simpson's rule gives 5.258495. 
E)  The Trapezoidal rule gives 5.007217 and Simpson's rule gives 5.008382. 
A)  The Trapezoidal rule gives 5.008090 and Simpson's rule gives 5.258495. 
B)  The Trapezoidal rule gives -5.008090 and Simpson's rule gives -5.008382. 
C)  The Trapezoidal rule gives 5.008090 and Simpson's rule gives 5.008382. 
D)  The Trapezoidal rule gives 5.007217 and Simpson's rule gives 5.258495. 
E)  The Trapezoidal rule gives 5.007217 and Simpson's rule gives 5.008382.

Question 11

Find the indefinite integral.

Accepted Answer

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

Question 12

Find the indefinite integral.

Accepted Answer

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

Question 13

Find the indefinite integral.

Accepted Answer

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

Question 14

Find the indefinite integral.

Accepted Answer

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

Question 15

Find the indefinite integral.

Accepted Answer

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

Question 16

Find the indefinite integral by making the substitution   .

Accepted Answer

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

Question 17

Find the definite integral.

Accepted Answer

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

Question 18

Use substitution and partial fractions to find the indefinite integral.   .

Accepted Answer

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

Question 19

Suppose the capitalized cost C is given by   , where   is the original investment, t is the time in years, r is the annual interest rate compounded continuously, and   is the annual cost of maintenance. Find the capitalized cost C of an asset forever if   . Round your answer to the nearest dollar. ​

Accepted Answer

A)  664,000 
B)  1,112,656 
C)  1,124,920 
D)  664,013 
E)  1,112,500 
A)  664,000 
B)  1,112,656 
C)  1,124,920 
D)  664,013 
E)  1,112,500

Question 20

Find   .

Accepted Answer

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

Find the indefinite integral.

Determine whether the improper integral diverges or converges. Evaluate the integral if it converges.

Determine whether the improper integral diverges or converges.

Use partial fractions to find the integral $Use partial fractions to find the integral .$ .

Determine whether the improper integral diverges or converges. Evaluate the integral if it converges.

Use partial fractions to find $Use partial fractions to find .$ .

Find the indefinite integral by making the substitution .

Find the indefinite integral.

Determine whether the improper integral diverges or converges. Evaluate the integral if it converges.

Apply the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral using 16 subintervals. Round your answer to six decimal places and compare the result with the exact value of the definite integral.

Find the indefinite integral.

Find the indefinite integral.

Find the indefinite integral.

Find the indefinite integral.

Find the indefinite integral.

Find the indefinite integral by making the substitution .

Find the definite integral.

Use substitution and partial fractions to find the indefinite integral. $Use substitution and partial fractions to find the indefinite integral. .$ .

Suppose the capitalized cost C is given by , where is the original investment, t is the time in years, r is the annual interest rate compounded continuously, and is the annual cost of maintenance. Find the capitalized cost C of an asset forever if . Round your answer to the nearest dollar.

Find .

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

Exam 8: Integration Techniques and Improper Integrals

Find the indefinite integral.

Determine whether the improper integral diverges or converges. Evaluate the integral if it converges.

Determine whether the improper integral diverges or converges.

Use partial fractions to find the integral .

Determine whether the improper integral diverges or converges. Evaluate the integral if it converges.

Use partial fractions to find .

Find the indefinite integral by making the substitution .

Find the indefinite integral.

Determine whether the improper integral diverges or converges. Evaluate the integral if it converges.

Apply the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral using 16 subintervals. Round your answer to six decimal places and compare the result with the exact value of the definite integral. ​ ​

Find the indefinite integral.

Find the indefinite integral.

Find the indefinite integral.

Find the indefinite integral.

Find the indefinite integral.

Find the indefinite integral by making the substitution .

Find the definite integral.

Use substitution and partial fractions to find the indefinite integral. .

Suppose the capitalized cost C is given by , where is the original investment, t is the time in years, r is the annual interest rate compounded continuously, and is the annual cost of maintenance. Find the capitalized cost C of an asset forever if . Round your answer to the nearest dollar. ​

Find .

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

Use partial fractions to find the integral $Use partial fractions to find the integral .$ .

Use partial fractions to find $Use partial fractions to find .$ .

Apply the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral using 16 subintervals. Round your answer to six decimal places and compare the result with the exact value of the definite integral.

Use substitution and partial fractions to find the indefinite integral. $Use substitution and partial fractions to find the indefinite integral. .$ .

Suppose the capitalized cost C is given by , where is the original investment, t is the time in years, r is the annual interest rate compounded continuously, and is the annual cost of maintenance. Find the capitalized cost C of an asset forever if . Round your answer to the nearest dollar.