Calculus II For Dummies, 3rd Edition

Chapter 8

Here’s Looking at U-Substitution

IN THIS CHAPTER

Understanding how variable substitution works

Recognizing when variable substitution can help you

Knowing a shortcut for using substitution with definite integrals

In Chapters 6 and 7, you discover how to evaluate a variety of indefinite integrals. This promises to make solving area problems framed as definite integrals much easier. But it still begs the question of how to evaluate indefinite integrals that don’t fit so nicely into the forms you know how to anti-differentiate.

In this chapter, you discover variable substitution (also called u-substitution), a very handy way to integrate functions that don’t appear at all friendly. I first show you how to use this method step by step, then take you behind the scenes to understand when variable substitution is likely to work well so you can feel confident when solving problems.

To wrap up, I provide you with a shortcut for using u-substitution when evaluating definite integrals.

Knowing How to Use U-Substitution

Variable substitution is especially useful when you’re faced ...