Trig Substitution - Calculus II - Handwritten Notes | MATH 1320, Study notes of Calculus

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Lecture 4 — Tria Supstitution The ota cases ae quile icky. These Induce: @O powes of tox w/ secx Switd, oll tomx 4 seoxl. This offen males it on eovlier case. x ( ton’ x dx = Stes x (sechxe I" dx > [ten x - Dhan sec x + tonx seein de = In [see x! ~ ton + T sec'x 4+C ® even powers fF tanx -/ odd powes of secx: switch oll ton? to secéx-| “ Iegeale by pols wf ve sex dx SH Dd all this integrale Funcliors = Ne xtat 4 Teig Subskhuker These are divect subshhtias: if x= 9), Ahr dx= Ql dt Some examples: Ex: \ dx \F x= tont , then dx= weet dt —_ x +) [6% (tu. (a getee det al ~ \ sect, at x=tont » t= tix > = (arctan x +E] = arctan * What did we lean? IF we seo x tl, Yer scleskhhing, xatont can Simplify | dx X= tot Be SK dx = sect dé