Trigonometric Integrals

# Trigonometric Integrals - TmcomanETRIc...

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Unformatted text preview: TmcomanETRIc INTEGRﬂLs _———__ \$0175 USEFUL IDENTITIES : (‘0le 4 .9!sz = I (Cost! = I-smzx‘, ETC.) I + inle = seclx goof 1x + I -.- csclx cost)! = iciicoséx) .9!sz -— tu-cosix) 73160100057337 C 'IN T5531”. 5 : um .- THEFE ﬁRE " nsoucnmo Faknows FOR 3 sw"x J x 1 S cosnxdxi’ S Jannx Jx mo 3 sea"): Jx, NEED mar BE nsnomzsn, BUT THESE OFTEN PRoWDE 7775 0057 EFFICIENT nEﬂNS 0F conPu-n’aus SUCH INTECRBLS. .m noommo To THE " BﬂSIc mBLE 0F wrest?an ' THERE Is one notes mar tones 0P arm» ENOUGH L amp I5 TRIcw ENOUGH ) mm you SHOULD REﬂEnBEl? tr: Ssechx = In Isecx +ln~xj +c HERE'S wI-IEPE Tms cones FIPDU .- » secx +In~x J 35a): X J 3 secx x a” * in”! sec'x + sax Jam: dx 3 sec): Ham: a: sew: “(max du =(secx4mux 4 seat): )Jx _ 34%. = InlMI4C . 4“. - Inlsecx-I-lmvxI‘C noRE EXBDPLES : ‘I 5 l. 8 5:» X COS XJX more : smES BNO cosmes war» a? 1.5057 ONE ODD PowER. q 5 3 Sm 3! cos XJX : S :3wa cos”): “stx = 3 3m”)! (cost)! 3: cos x J)! ‘l g t = 35:» v u-sm x) wstX a: Squ d.“ = cos X Jx = S A” La~u")"cl« : SMHL I ~~2Az‘luq)JM COULD use a neoucnam Fotnum, on 2 Seas xe = Sill-N051! )Jx : {:3le 4 i Seesaw/x 3:41)! (In: ZJX (1001.0 036 A tEDuc'no» Panama, on M 3 sm’x J! 2. 3 5m I: switch: = ELI-(051)!)SwXJY “3505” d“: -\$WXJX l S .91le cos xdx NOTE : smes AND CoswES, 130771 EVE» PowERS. Q 1 3 Sun Y COS Xc‘x : S \$l~1X(l-\$lw1)()4x 7.. S Slle-qux Jx Now use REDUCTION :9 Few nnES_ n~I - n-z 33m."xe = .. #SIM 3:50;): 4 93459» Xc‘x 0:1 : 35"»!xe = -j_-5I~xcosx 4 i 31:1): . 35waccosx + ix +C ‘i 3 3 2 nzl-l : Sslvoxe:-{;swx{osx +7851px¢1x 3 3 J. .. é Suu KCDSX + ;[.a_sa~¥co5x 43",):3 +C. 3 3 i : - fist» xcasx .. Faustx + 8,! +C THUS 3 J. SSnn'x castxe : [- 3f swartasx + 1‘”) ‘ l” q 5‘“ x “9‘ %51~X(o\$¥ + 1%" 3 “- ~ J- EILSCN3XCOSX - éSluXL‘OSX 4 8X 4C. ﬂLTEIi’NnﬂvE Sowﬂam : l 3 5m"): cos xe = Betti—aslx))(tu4m¢w)¢lx l 7. = 753 ("‘0‘ “’4‘ 3 \$39» ax Jx = .1, 3%.»;me : ‘LBU-Cos‘lx)Jx= é(xv;’isw‘1x)-FC .L : #x. 31 sm‘ix +C If 3 vazx sec x 4;: NOTE ; mmaENTS nND SECBNTS won-1 an EVED Paws!) of 56mm: '- Z 3 but): 334 x sec xe = 3 )mu‘x (1+ kwlx)\$€clix : .u: 7‘90)‘ z 3 but): sec x (secx’muxulx ‘~ 3 (Stair-13566,)ll5tcxianJJx : M: secx d4: grandma): 5 3 3 «Al—.m’Ja = 3 m"—«‘)Ju= g4 jg +c : .5' 3 secx — 4-3ch +c J. 5 .3 '7. 3 5w 7): cos 3x o’x was one Is miner. REC/9H,: Swlﬁ-B): swﬁcosB —cosﬁsauB 3w (3+6) = 31:06 cos B 4- £053 540 8 HDD Snow-:3) + swmm) = lswﬁ cos B so Smﬂ cos B = i (3!» (ﬂ—BH swmrm) was» A=7x n~o 8: 3x 171:: 8560065 \$1~7st3x : iLSwLiX + swmx) 3 SM'lxcos 3’xe = 1" 3(sm'4x +3mI0x)Jx = 3L: L- {1- 4:0st - {aces/OX] +C .- — frost/x — 5305on +C r. 3. 3 gag-lb: : assequu=2lnjs¢cu+lnuMI+c M_r; :Q'n’S€cﬁ+}'ﬁwﬁ)+C L/’ m n n W x G.— at. I L/5 m n h x k x H REDUCTION FannULﬂ " "'2 . n—z Ssec. xclx : ;-_’-,-\$ec xh~x+-:—_—f Ssec xe .- s :- secxhamx + 3‘; 3 sechx - 3%;xe i- secx ’19»): - 3'; Ssecxdx = isech-nwx .. ilnlsecx +791NXI +C ...
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Trigonometric Integrals - TmcomanETRIc...

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