3.4 Improper Integrals

In this lesson, you will learn about improper integrals.

Lesson Objectives

  • Recognize an improper integral: integration over an infinite interval or integration over an infinite discontinuity.
  • Recognize that an improper integral is a limit of a definite (proper) integral.
  • Understand the difference between convergence and divergence of improper integrals.
  • Evaluate improper integrals by constructing and evaluating appropriate limits.
  • Use the basic comparison test to establish the convergence or divergence of improper integrals.

Lesson Content

View all of the following instructional videos. These will help you master the objectives for this module.

  1. YouTube video: Improper Integral – Basic Idea and Example
  2. YouTube video: Improper Integral – More Complicated Example
  3. YouTube video:Improper Integral – Infinity in Upper and Lower Limits
  4. YouTube video: Comparison Test for Improper Integrals
  5. YouTube video: Improper Integrals
  6. YouTube video: Improper Integral with Infinite Discontinuity at Endpoint
  7. YouTube video: Improper Integral with Infinite Discontinuity at the Middle

Lesson Readings

The following required readings cover the content for this module. As you go through each reading, pay close attention to the content that will help you learn the objectives for this module.

  1. Improper Integrals
  2. Improper Integrals  (type 1 improper integrals, type 2 improper integrals, direct comparison test, limit comparison test)
  3. Improper Integrals
  4. Improper Integrals  (by Dr. Marcel B. Finan from Arkansas Tech University)

Lesson Practice Exercises/Activities

Make your way through each of the practice exercises. This is where you will take what you have learned from the lesson content and lesson readings and apply it by solving practice problems.

  1. Improper Integrals  (27 problems with hint and answer)
  2. Improper Integrals  (answers and solutions provided)

Additional Resources

Below are additional resources that help reinforce the content for this module.

  1. Improper Integrals
  2. Improper Integrals  (definition of an improper integral of type 1 & 2, comparison theorem for improper integrals)
  3. Improper Integrals  (two types of improper integrals, general strategy for improper integrals, infinitely long intervals of integration, functions undefined at an endpoint of the interval of integration)