In this lesson we are going to talk about Integration of Trigonometric Functions. The prototypical examples of these integrals is: we will have an integral and some power of sine and some power of cosine. The important thing to focus on here is what those powers are. We want one of those powers to be odd. Important thing is to find one of those numbers and to make it the odd. If they are both odd, we can just pick one. The one that is odd, what we do with it, is we are going to make a substitution and let U be the other one. Check the video for further steps.
Remember to check which of the powers is odd. Then let u be the other one. (E.g. if
you have cos5 x, then use u = sin x.)
If both powers are even, use the half-angle formulas.
If you have an even power
of secant, use u = tan x. If you have an odd power of
tangent, use u = sec x.
If you have an odd power of secant and an even power of tangent, then follow this process:
Convert tangents to secants, two
at a time, using tan² +1 = sec²
. Youll end up with odd powers of secant.
Use integration by parts twice (u
= secn−2 x, dv = sec²
x dx) to cut down from ∫ secn
x dx to ∫ secn−2
x dx, so you eventually get back to ∫ sec
x dx. Then remember the formula:
Integration of Trigonometric Functions
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.