Question 1

Find the indefinite integral. ​   ​

Accepted Answer

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

Question 2

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   ,   ,and   .Round your answer to the nearest dollar. ​

Accepted Answer

A) 676,400 
B) 1,463,400 
C) 1,497,141 
D) 676,420 
E) 1,463,000 
A) 676,400 
B) 1,463,400 
C) 1,497,141 
D) 676,420 
E) 1,463,000

Question 3

Find the indefinite integral. ​   ​

Accepted Answer

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

Question 4

Find the area of the region bounded by the graphs of   ,y = 0,x = 0,and x = 1. ​

Accepted Answer

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

Question 5

Use partial fractions to find the integral   . ​

Accepted Answer

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

Question 6

A hydraulic cylinder on an industrial machine pushes a steel block a distance of x feet   where the variable force required is   pounds.Find the work done in pushing the block the full 5 feet through the machine.Round your answer to three decimal places. ​

Accepted Answer

A)    ft.lbs 
B)    ft.lbs 
C)    ft.lbs 
D)    ft.lbs 
E)    ft.lbs 
A)    ft.lbs 
B)    ft.lbs 
C)    ft.lbs 
D)    ft.lbs 
E)    ft.lbs

Question 7

Let   for   and   .
​  
-​Find an expression for   in terms of   only.

Accepted Answer

The answer of Let   for   and...

Question 8

Find the indefinite integral. ​   ​

Accepted Answer

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

Question 9

Use integration tables to find   . ​

Accepted Answer

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

Question 10

Use substitution to find the integral   . ​

Accepted Answer

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

Question 11

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

Accepted Answer

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

Question 12

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 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   . ​

Accepted Answer

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

Question 16

Find the indefinite integral   . ​

Accepted Answer

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

Question 17

Find the indefinite integral by making the substitution   . ​   ​

Accepted Answer

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

Question 18

Use integration tables to find   . ​

Accepted Answer

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

Question 19

Evaluate the limit   using L'Hopital's Rule if necessary. ​

Accepted Answer

A)    
B)    
C) 1 
D) 0 
E) does not exist 
A)    
B)    
C) 1 
D) 0 
E) does not exist

Question 20

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

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 , ,and .Round your answer to the nearest dollar.

Find the indefinite integral.

Find the area of the region bounded by the graphs of ,y = 0,x = 0,and x = 1.

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

A hydraulic cylinder on an industrial machine pushes a steel block a distance of x feet where the variable force required is pounds.Find the work done in pushing the block the full 5 feet through the machine.Round your answer to three decimal places.

Let for and . -Find an expression for in terms of only.

Find the indefinite integral.

Use integration tables to find .

Use substitution to find the integral .

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

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

Find the indefinite integral.

Find the indefinite integral.

Find .

Find the indefinite integral .

Find the indefinite integral by making the substitution .

Use integration tables to find .

Evaluate the limit using L'Hopital's Rule if necessary.

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

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Infinite Series

Parametric Equations, Polar Coordinates, and Vectors

Mechanical Ventilation and Sedation: Assessment, Medications, and Complications

Filters

Exam 8: Integration Techniques, L'Hôpital's Rule, and Improper Integrals

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 , ,and .Round your answer to the nearest dollar. ​

Find the indefinite integral. ​ ​

Find the area of the region bounded by the graphs of ,y = 0,x = 0,and x = 1. ​

Use partial fractions to find the integral . ​

A hydraulic cylinder on an industrial machine pushes a steel block a distance of x feet where the variable force required is pounds.Find the work done in pushing the block the full 5 feet through the machine.Round your answer to three decimal places. ​

Let for and . ​ -​Find an expression for in terms of only.

Find the indefinite integral. ​ ​

Use integration tables to find . ​

Use substitution to find the integral . ​

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

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

Find the indefinite integral. ​

Find the indefinite integral. ​ ​

Find . ​

Find the indefinite integral . ​

Find the indefinite integral by making the substitution . ​ ​

Use integration tables to find . ​

Evaluate the limit using L'Hopital's Rule if necessary. ​

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

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Infinite Series

Parametric Equations, Polar Coordinates, and Vectors

Mechanical Ventilation and Sedation: Assessment, Medications, and Complications

Filters

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 , ,and .Round your answer to the nearest dollar.

Find the indefinite integral.

Find the area of the region bounded by the graphs of ,y = 0,x = 0,and x = 1.

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

A hydraulic cylinder on an industrial machine pushes a steel block a distance of x feet where the variable force required is pounds.Find the work done in pushing the block the full 5 feet through the machine.Round your answer to three decimal places.

Let for and . -Find an expression for in terms of only.

Find the indefinite integral.

Use integration tables to find .

Use substitution to find the integral .

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

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

Find the indefinite integral.

Find the indefinite integral.

Find .

Find the indefinite integral .

Find the indefinite integral by making the substitution .

Use integration tables to find .

Evaluate the limit using L'Hopital's Rule if necessary.

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