Improper integrals

The  exercise appears under the Integral calculus Math Mission. This exercise introduces improper integrals.

Types of Problems
There are two types of problems in this exercise:


 * 1) Determine which are improper integrals: This problem presents several integrals that may be improper. The student is asked to determine which are improper, which are not, and indicate the answer in the table.Impint1.png
 * 2) Find the value of the improper integral: This problem presents an improper integral. The student is asked to find the value of the improper integral and provide the answer as indicated.Impint2.png

Strategies
Knowledge of integration and limits are encouraged to ensure success on this exercise.
 * 1) The two main types of improper integrals both happen at asymptotes.
 * 2) An integral is improper if one of the bounds is infinite. This will be finite only when the y-axis is an asymptote, but not all the time when the y-axis is an asymptote.
 * 3) An integral is improper if it has a vertical asymptote between the lower and upper bounds of integration, or if one of the bounds is a vertical asymptote.
 * 4) An improper integral is performed by replacing the infinite value by a variable, performing the integral, then taking a limit.
 * 5) An improper integral can be done informally by "plugging" in infinity (taking a limit mentally).

Real-life Applications

 * 1) Integrals can be used in physics to find the total distance travelled by objects.
 * 2) Integrals can be used in economics to find the total profit or cost of business ventures.
 * 3) Many times situations where one is looking for a "total" can be performed with integration.
 * 4) Improper integrals occur in situations with rational functions.
 * 5) There are interesting thought experiments that can be created with improper integrals, such as a tub that cannot hold enough paint to paint itself.