7.4 Integrations by Basic (u) Substitutions

In this lesson, you will learn to use substitution to obtain an easier integral to evaluate.

Lesson Objectives

Upon completion of the lesson 7.4, you will be able to:

• • Recognize the use of the chain rule in making substitutions in integrals.

  • Evaluate indefinite integrals using basic substitutions.

  • Evaluate definite integrals using basic substitutions.

Lesson Content

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

• 1. Change of Variables (substitution) [University of Houston]

  2. YouTube videos: Integration by U-substitution Antiderivatives

• 1. Definite integral:

• 1. Indefinite integral:

• 1. YouTube video: Definite Integral with Substitution (Example with Trigonometric Function)

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. u-Substitution - Changing variables in integrals [Paul's Online Math Notes]

2. Integration by Substitution [Eastern Iowa Community Colleges]

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. Substitution Rule for Indefinite Integrals [Paul's Online Math Notes] (problems with solutions)

  2. Note: Do problems #1 - 7, 10, & 13.

  3. The u-substitution; change of variables [University of Houston] (with answers and solutions)

  4. Visual Calculus - Integration using Substitution [University of Tennessee] (solutions provided)

  5. Note: Do problems #2, 4, 7, 9, & 10.

  6. Visual Calculus - Integrations using Substitution [University of Tennessee] (solutions provided)

  7. Note: Do examples #1, 2, 4, 7, & 12. (Flash or Java needed)

  8. Substitution Rule for Definite Integrals

  9. Note: Do problems #1, 2, 3, 7, 8, 9, & 10.

Additional Resources

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

• 1. More Substitution Rule [Paul's Online Math Notes] (solutions provided)

  2. Note: Do problems # 1, 4, 7, 9, 10, & 13.

  3. Integration by substitution

  4. YouTube videos: Integrating a definite integral by substitution

• • Example 1

  • Example 2

  • Example 3