In this lecture you will learn the Integration of Trigonometric Functions. Professor Murray will teach the important equations and go over Odd Powers and Even Powers. You will also review Half-Angle formulas to speed up some examples.
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.