Calculus II Workbook For Dummies

Chapter 8

Here’s Looking at u-Substitution

IN THIS CHAPTER

Understanding how to do variable substitution step by step

Integrating the product of a function times its derivative

Recognizing more complex integrals that you can evaluate with variable substitution

Evaluating definite integrals by changing the limits of integration

Variable substitution (also called u-substitution, or u-sub for short) is a relatively simple way to integrate complex functions, especially products of functions and compositions of functions.

In this chapter, you first discover the how of variable substitution. Then, I show you the simplest type of function that you can integrate using variable substitution: functions that are the product of a function and its derivative. Next, I show you the more complicated case: functions that are the product of a composition of functions and the derivative of the input function.

After that, you see how when you evaluate definite integrals using variable substitution, you can often make your work easier by changing the limits of integration.

Understanding the How of ...