Learn the intricacies of trigonometric substitution in this comprehensive 39-minute video tutorial. Discover when and how to apply this integration method, which simplifies integrals by leveraging right triangle relationships. Explore various types of integrals suitable for trig substitution, including those with and without square roots or perfect squares. Gain insights into selecting the appropriate substitution (sine, tangent, or secant) based on the integral's form. Understand the underlying principles of trig substitution and master a step-by-step approach to solving problems. Follow along as the instructor demonstrates how to set up, simplify, integrate, and back-substitute to obtain final solutions. Learn to construct reference triangles and apply trigonometric identities effectively. By the end of this tutorial, you'll be equipped with the knowledge and skills to tackle complex integrals using trigonometric substitution confidently.
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
