This course on trigonometric substitution teaches students how to simplify integrals by leveraging the relationships in right triangles. The learning outcomes include understanding when to use trig substitution, identifying which trig substitution to apply, setting up and solving trig sub problems, and back-substituting the integrated value. The course covers sine, tangent, and secant substitutions, and provides a step-by-step approach to tackle trigonometric substitution problems. The intended audience for this course is individuals looking to enhance their integration skills and tackle integrals involving complex values.
Overview
Syllabus
// What is trig substitution?.
// When to use trig substitution?.
// What kinds of integrals use trig substitution?.
// What to do when there’s no square root?.
// What to do when you don’t have perfect squares?.
// What do trig substitution integrals usually look like? Which trig substitution to use? (Examples of sin substitutions, tan substitutions, and sec substitutions).
// Why trig substitution works?.
// How to set up for a trig substitution problem?.
// How to solve trig substitution? How to do sine substitution?.
// Step 1. Identify that it’s a trig sub problem.
// Step 2. Decide which trig substitution to use.
// Step 3. Do the setup process for trig sub.
// Step 4. Make substitutions into the integral.
// Step 5. Simplify the integral using whatever methods you need to, then integrate.
// Step 6. Back-substitute to put the integrated value back in terms of x, instead of theta..
// How to build your reference triangle.
Taught by
Krista King
