Here’s a helpful tip. When things are complicated, us a substitution rule to make things easier!
In particular, Trigonometric Substitution, also called Inverse Substitution, is a way for us to take a difficult radical expression and transform it into a manageable trigonometric expression.
The idea is to use our trig identities and our understanding of special right triangles (SOH-CAH-TOA) to simplify our integrand by substituting an expression into the integral in which a new variable is a function of the old one.
And will see the connection between Inverse Trig Functions and also the Pythagorean Theorem, to make our trig substitutions.
Understanding Trig Substitutions for Integration
More importantly, we will see a connection between the length of the base of a right triangle and its hypotenuse.
There are three types of Trigonometric Substitution, and we will walk through an example of each type, all while reviewing important concepts from pre-calculus as we go.
Additionally, we will quickly see how these substitutions help simplify our radical expressions, and enable us to solve problems for both indefinite and definite integrals.
Trig Substitution Video
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