University:
University of Central Florida
Course:
MAC 2312 | Calculus with Analytic Geometry II
Academic year:

2023
Views:

245

Pages:

5
Author:

Maria

3.2. Trigonometric Integrals I) ' sin x cask xalx A) K is add (power of cos x is add) 1) Split off one power of cos x 2) Convert remaining powers of cos x into sinx using. cos²x = 1-sin²x 3) Int by sub with u = sinx; du cas x dx B) Power of sine is odd 1) Split off one power of sin x 2) Convert remaining sines into cosines using sin x = 1-cos²x 2 3) Int by sub u= cos x; du-sinx dx C) Both 1) use * cos^2 x = (1 + cos 2x)/2 * and * sin^2 x = (1 - cos 2pi)/2 * con*pi*tnot I) integrate tan^j x * sec^k x dx d/dx (tan x) = sec^2 x (sin^2 x)/(cos^2 x) + (cos^2 x)/(cos^2 x) = 1/(cos^2 x) A) Power of see x is even. 2 1) Split out sec x - 7tan^2 x + 1 = sec^2 x 2) Convert remaining powers of see x into ton x using sec²x = 1 + tun'x 3) Int by Sub with u tomx, du=sec²x dx x Secx Secx found B) Power of tan x is odd. 1) Split out a seex lan x 2) Convert remaining powers of tan x into seex using tan^2 x = sec^2 x - 1 3) Int by Sub u seex, du see x town x dx C) Power of sec x is add and power of tan x is even Ⅲ) Scotxesex olx k Same rules as ftan'x secx dx (but sometimes there is - ) IV) Other combinations can be reduced to other cases using trig identities