Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

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 & Tips

Terms you should be able to define: trigonometric triangle, trigonometric substitution Mini-Lectures and Examples

Supplemental Resources (optional)

rev. 2021-02-06