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S = contains supplemental resources
Course: Calculus II
Topic: Integration Techniques
Subtopic: Trigonometric Substitutions

Overview

In this lesson we learn to evaluate integrals of certain rational expressions, by transforming them via substitutions obtained from trigonometric triangles, into a trigonometric integral and then applying those processes to finish off the evaluation. This technique is called the method of trigonometric substitutions. The substitutions are based relationships obtained by three trigonometric triangles which you should memorize.

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 8.3.1 Apply the three trig triangles used in the method of trig substitutions (and have them memorized)
• 8.3.2 Use an appropriate trig triangle to transform an integral into a trig integral
• 8.3.3 Employ algebraic techniques to simplify or rewrite an integral so that the method of trig substitutions can be applied

Terminology

Define: trigonometric triangle, trigonometric substitution

Supplemental Resources (recommended)

One of the difficult aspects of this material is to know which integration technique to use. Here are some resources that may help. If you find better ones please share in class!

Supplemental Resources (optional)