Calculus II For Dummies, 2nd Edition

Chapter 7

Trig Substitution: Knowing All the (Tri)Angles

In This Chapter

Memorizing the basic trig integrals

Integrating powers of sines and cosines, tangents and secants, and cotangents and cosecants

Understanding the three cases for using trig substitution

Avoiding trig substitution when possible

Trig substitution is another technique to throw in your ever-expanding bag of integration tricks. It allows you to integrate functions that contain radicals of polynomials such as and other similar difficult functions.

Trig substitution may remind you of variable substitution, which I discuss in Chapter 5. With both types of substitution, you break the function that you want to integrate into pieces and express each piece in terms of a new variable. With trig substitution, however, you express these pieces as trig functions.

So before you can do trig substitution, you need to be able to integrate a wider variety of products and powers of trig functions. The first few parts of this chapter ...