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Calculus II

by: Maximilian Turcotte

Calculus II MATH 112

Maximilian Turcotte

GPA 3.7


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Class Notes
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This 3 page Class Notes was uploaded by Maximilian Turcotte on Monday October 5, 2015. The Class Notes belongs to MATH 112 at Colgate University taught by Staff in Fall. Since its upload, it has received 25 views. For similar materials see /class/219589/math-112-colgate-university in Mathematics (M) at Colgate University.


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Date Created: 10/05/15
Tricks for Trigonometric Integrals f sinm 05 cos x dx m odd 1 cos2 xm 12 cos x sinx dx u cosx 1 ugm 12u du 71 odd fsinmx sin2 x 12 cosxdx u sinx fum ug 12du 2 mm both even sin 05 1 cos 2x 1 2 cosgx 1 cos 295 f seem x tan x dx m even tan2 x 1m 22 tan 05 sec2 x dx u tanx u2 1m 22u du 71 odd secm 1 95sec2 x 1 12 secx tanx dx u secx fumilcuQ 1n712du sin 05 m odd 71 even dx cosmn x sin 05 d cosx x usinx 1 sin2 xmn12 and wait for partial fractions 7 sinAB sinAcosBsinBcosA sinA B sinAcosB sinBcosA cosAB cosAcosB sinAsinB cosA B cosAcosBsinAsinB sinAcosB sinA B sinA B sinAsinB COSA B cosA B cosAcosB cosA B cosAB Some possibly useful formulas V Azdz V 7rr2dx V 27rrhdr W Fdx 1 00 00 m 7 7L 1 7 a 7 Zm7 lzllt1 e 7 allm 0 n0 ln1 i0 innil l llt1 sin i0 71 2 all ix 7 m m 7 7 1 n 0 271 1 00 00 71 n arctanz 71 z2 1 7 lt 1 cosz Z 7 2 7 all z n0 0 un7b sinZA l17cos2A integrand in 7 am 1 b z 7 2 a 1 integrand in em u em cos2 A 51 cos 2A 1 arcsin C integrand in a2 7 2 z asin0 a gm 1 a m integrand in 2 a2 3 z atan0 72 a2 arctan C integrand in 2 7 a2 z asec0 dm 1 C 7 arcsec 7 m a a m w 7 m m MM 79mm 7 Jams 7gltzgt2gtdzgt area area dzy 373 1 1 w T s 7 a Wt ylttgtgt2dt 7 Eflt gtltagtltas 7 a dt Zan converges if lim lt 1 quot l woo anl lt 1 or lim Hoe an1 an i an an7 bn gt 07 a 7 07 oo Zan converges ltgt an converges 1 00 n a Z converges ltgtpgt1 lrllt1nar 717T 00 N an decr7 lim an 0 271 an converges and Z71nan 7 271 an lt LA1 h n1vyn1 mn 1 I17 39 1 fltmmynh Tn 1 210m1 1 quot391 2flt n71 1 Mn we mm Sn gm 4fz1 2mg 4f90n71 mm


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