Calculus II For Dummies, 2nd Edition

Chapter 5

Making a Fast Switch: Variable 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

Unlike differentiation, integration doesn’t have a Chain Rule. This fact makes integrating compositions of functions (functions within functions) a little bit tricky. The most useful trick for integrating certain common compositions of functions uses variable substitution.

With variable substitution, you set a variable (usually u) equal to part of the function that you’re trying to integrate. The result is a simplified function that you can integrate using the anti-differentiation formulas and the three basic integration rules (Sum Rule, Constant Multiple Rule, and Power Rule — all discussed in Chapter 4).

In this chapter, I show you how to use variable substitution. Then I show you how to identify a few common situations where variable substitution is helpful. After you get comfortable with the process, I give you a quick way to integrate by just looking at the problem and writing down the answer. Finally, I show you how to skip a step when using variable ...