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Calculus IV
15.Functions of Several Variables
16.Multiple Integration
17.Vector Analysis
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:

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)

Video: Trigonometric Substitutions, Selwyn Hollis's Video Calculus

Lesson: Trigonometric Substitution - Another Change of Variable, Dale Hoffman's Contemporary Calculus