2.3 Trigonometric Substitutions

In this lesson, you will learn about trigonometric substitution.

Lesson Objectives

  • Recognize the binomials that lend themselves to trigonometric substitutions.
  • Complete the square in order to re-write a quadratic polynomial in the form of a trigonometric substitution binomial.
  • Evaluate integrals using trigonometric substitution.

Lesson Content

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

  1. YouTube videos: Trigonometric Substitution
    Example 1:
    – Part 1:

    – Part 2:

    Example 2:

    Example 3:  – Part 1:

    – Part 2:

    Trigonometric Substitutions – More examples (using trigonometric substitution to integrate radicals)

  2. YouTube videos: Integrals: Trig Substitution 1 (example of using trig substitution to solve an indefinite integral)
  3. YouTube video: Integrals: Trig Substitution 2 (another example of finding an anti-derivative using trigonometric substitution)
  4. YouTube video:Integrals: Trig Substitution 3

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. Trigonometric Substitution Intuition
  2. Trigonometric Substitution. (with exercises and answers/solutions)
  3. Trigonometric Substitutions.
  4. Lecture 32: Trig Substitutions.


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. Trigonometric Substitution (with exercises and answers/solutions)
  2. Integration Using Trigonometric Substitution


Additional Resources

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

  1. Trig Substitutions
  2. Integration Involving Trigonometric Functions and Trigonometric Substitution(with review of trigonometric integrals)
  3. Trigonometric Substitutions