Skip to Main Content
Calculus II For Dummies, 2nd Edition
book

Calculus II For Dummies, 2nd Edition

by Zegarelli
January 2012
Intermediate to advanced content levelIntermediate to advanced
384 pages
8h 37m
English
For Dummies
Content preview from Calculus II For Dummies, 2nd Edition

Chapter 5

Making a Fast Switch: Variable Substitution

In This Chapter

arrow Understanding how variable substitution works

arrow Recognizing when variable substitution can help you

arrow 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 ...

Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Calculus II For Dummies, 3rd Edition

Calculus II For Dummies, 3rd Edition

Mark Zegarelli
Calculus II

Calculus II

Chris Monahan

Publisher Resources

ISBN: 9781118161708Purchase book