Sometimes it is necessary for us to use trig identities to integrate certain combinations or powers of trigonometric functions.
Trigonometric Integrals, also known as advanced trigonometric integration, takes a complex trig expression and breaks it down into products of easier to manage trigonometric expressions all while using our known identities. In other words, they are reduction formulas for integration.
The trick to doing this is understanding the dominate trig function and the power or exponent involved.
We will start with using a little ingenuity in order to integrate sec(x).
According to Paul’s Online Notes, we will multiply the numerator and denominator by a term in order to put the integral into a form that can be integrated.
In other words, as long as we multiply by a factor of 1, we can “add” a necessary component into our integrand.
Sneaky!
Formulas for Evaluating Trigonometric Integrals
Don’t worry; everything relates back to the Pythagorean Identities, which we will review, which helps to make thinks easier. And I will also remind you about our six basic trig integrals, as well as how and when to use half-angle identities and U-Sub to simplify our integrand as well!
Then we will learn some funny sayings (i.e., OSUC, OCUS, OTUS, and ESUT) to help us remember how to manipulate trig integrals that have odd or even exponents.
These silly sayings will help identify the dominate trig function and the power or exponent involved that I talked about earlier!
Lastly, we will walk through six examples, one example for each type, all while still using our other integration skills such as U-Substitution and Integration by Parts, in order to master these advanced Trig Integrals.
Advanced Trigonometric Integration Video
Get access to all the courses and over 450 HD videos with your subscription
Monthly and Yearly Plans Available
Still wondering if CalcWorkshop is right for you?
Take a Tour and find out how a membership can take the struggle out of learning math.