8/12/2019 hitung integral

1/33

ffiffis.

8/12/2019 hitung integral

2/33

k%d,&HaffiHM&ru

NTE HIT

UNG GRAL

ffiffi,ffitr-$*'i.tS-ffi*ffiffiffiffiffiFiHliif,ii:, rii,i.I#:i*ii9rTl,?rWWriFx+,:i::iiisi'r.Bi.{;ii!"{i11,.if.i

8/12/2019 hitung integral

3/33

: .

8/12/2019 hitung integral

4/33

'*i'N #.+,,.:: Am.I.rfi-E*#brl.'t.':&r=:t'rl it4:"

-.

utculu*ooi f,1\}

I'1.,"l.:'"t: ]lttuluu gtutqrruutl'td:j,;

8/12/2019 hitung integral

5/33

HITUNG Drs.Wardiman

8/12/2019 hitung integral

6/33

INT'EGRA!Penerbit: Jln. Tamansiswa PT. HANINDITA Yogyakarta

101 B- GRAHA 6

WIDYA .0274l- 8N22,88193Ttta lgtak : T. lran Disein kulit muka : Hanindita

@ Hak Pengarang dan Penerbit dilindungi oleh Undang-undang.CetakanKetiga, Juli1987axclttolcli :

PT. HANINDITA OFFSET-

Yogyakarta lsi diluar tenggung iawab percetakan.

8/12/2019 hitung integral

7/33

UVINV9NSd V.I.VT t]

8/12/2019 hitung integral

8/33

'mq?ilet aPor?w-?Potzut uo*uap lonsas tuot uop 'tolns tuof todutos ouoqtapas tuo{

uop ,loospos-lrrls lnt uollosqnq uoqnqtad untuoqwaw 1n7unlrlltrl-lulnt

! dt

nto, orror)'l!#T::#r#loosloos totoltd-toluad

unlmsala(uantuolop lmlotuaw

un1 ,otutttltly!u! nlng'umlas

lq uqo1,nlpnlnqtotu8uaytuldwosryluntad uop

lnun molasWolDlp uotlo,orfpwe\tmuwtralnsatl-uotolnsfil otuomatwolop tw[.tunpl otlow'lottalur lutt

to;oselelucd qoruot-tlotuoc'otn[ uoluaqrp apota,u-e?opu noro ,yoay1to4tuo{ 'onqwad opodaq Wsorl owydt t1o{.uoq-ryKwq uotldom

-eol qeto 'Ws-loos uoryosapfuaw

uqdutouatl opod uolyoq ruorl pteq rfiryuotuep uqueqp tuoi{, uotlopsal-uoqolos?rl uolntaqwed

rytwn uqwntyp otnl wdop 'olqoqa oilsrsntry-Dttsrsoqowtuo( 'pttatul tuu1t1

{uxal qoples nlopd-totwed

8/12/2019 hitung integral

9/33

'nqaslet uotulnserl-uotolnsarl'!u!

Zg6l ,ouolof,SoyslpuaduDnuDIuowrP,toA['aotuoleuau pdop ottlas

unry olrsrsotry-Dilsrsaqow qep-mlopd uqqn,qwa'tuot'rlotuauey

umts qofmsrrswP o,,.qsoqoy{-otttsTsoqotu

uoVu?qwau r?nsouofit?t so1tlt1t

-o*rlsoqilt-ur, ?potinu-qa[ucut-1oos

8/12/2019 hitung integral

10/33

ISI HVIJVO N

8/12/2019 hitung integral

11/33

u?ur?lBtluvrNvDNad vJ.v) uYrcvotst u Tgvg

ISnvtlnu*snnnu UVSV(I

'IVUCATNT 'lnlueuel4qle-6a1u1'ZserEelulsnutu-snunuFos-leos"" ":" "':""

":" ' I St t ""lBos-lBos ""' 8z {v8llrsvucarNMooJ,3n0

Inlueq 'Bp.6.a1ulpup xxP :'q

le6alul utulsxusocpup{ntueq

: ,,,sri ures xxp uup

8/12/2019 hitung integral

12/33

u,Elc0gxucesocs:

x xp 't1u.6e1ul Iuup

{nlueg ,,9t,xrus03 xu xpfu*xp xu uls *.'u"o, fxp xu soc xur

6t, '?,;u-Ea1u1

uutuep uu>;uun8Buatu Isnlqsgns ' 'BEnlllsqnsl$unJ

JDqBfie ' '" .g....p1embuoEpguuEuapFnlnsqns O, gV'cprEeluJlrep ;sun3 r;eccdl?uors8.r'pprEalul

8/12/2019 hitung integral

13/33

lrep r6un;-r$un; [BuorsuJn 6t Ig.'e. lsuncJsl.toIsBJuBp uls x uBp soc x '

" ., ....[8os_Fos.....aL Lu

8/12/2019 hitung integral

14/33

BAB III

8/12/2019 hitung integral

15/33

INTEGRASI FUNGSI HIPERBOLIK l.Rumus-rumus dasar fungsi hiperbolik 2.Rumus-rumus dasar integral dari fungsi hiperbolik 3.

Substitusi fungsi hiperbolikSoal-Soal BAB IV

RUMUS_RUMUS REDUKSIl.Rumus reduksi untuk Binomial DifferensialSoal-Soal2. Rurn us red87E788 9l949797100102105r06160lvtuk trigonbme tri kdi fferensialSoal-SoalBABVDAFTARuksiunPENYELESAIAN SOAL_SOAL UJIANPUSTAKA

8/12/2019 hitung integral

16/33

8/12/2019 hitung integral

17/33

IgVSNSNWNU.SNruNU UVSVO ]VHSSINI '1

]vu9:IrNt)tvt nrNlrHt )trNHrcNt wucsrNt (BIE6J

(x) etlg tnqasTp .r (x) ntens alyu (1erta1u1 TrBp J nfuatrlrrp'(x) 1stun3 tuepasEued; @ (x) ledunduau nere lngesTp 1erta1u1 alTfe^1rap 'ueffii rtet '5 rd (x) - I '(x) nruCiiJr ) -

TrapuT 1arta1u1 {Bl -raf r,r.rerl,r.ft+*P,Ltr*)nfensE*= -5 lstunJ T

qafppe x)+ Eue(lertatuT t/InqBtaITp IBpTt 1et8un1 t

8/12/2019 hitung integral

18/33

letaqas>1e1ntuafralTrpP J=_(x) qoluoc.'r*

: ' -tleTo = I$ )(Drx1- (5=e Z*ertegl'

ferta1ul IB? -ra?

nluofTr?p J (x) _ E ZxledepslTnlTp B;rcas umumex

+ D tupfsuoc) Jo (uoltertaluT Inf,uOueqele(uau lertaluy:1e1nfualral TrBp J tue{ . Buerslp O -Tp 'tuerequae (x),

eTTni}p uetuap {nluaq : ,t(x)xP 'D+rx=*PZ,: Tpaf

rsvucSrNt snnnu-snwnu .z.t;'l";T'tr .T

8/12/2019 hitung integral

19/33

v( eJC+(x1J=xP(x)t,

'xp { (,,rf(n+xp = *on] (

)* (_ xedeltas

8/12/2019 hitung integral

20/33

4.

8/12/2019 hitung integral

21/33

5.6.7.8.9.10.11.tr:13.t4.15.L6.t7.18.19.

* ,l;'=

#T + c,m

I -r' F ="'lul*' fuou=#*"+c,a;'o,1

) [.'ou=.u*..f"t"udu=-cosu=c.["."udu=slnu+c. frr"du=rnl"""ul*..

8/12/2019 hitung integral

22/33

f".,,du =ln lsln u[ * ..(""" Iu du =ln.tse.1"o"..u + tg Uf r-ctg1"""'U dU = 1r, |"o"""Uu du = cs u + c.1"."""'udu=-crsu+c.t"..,tg U dU = sec U +C.("o"."(du1u )Uctg

8/12/2019 hitung integral

23/33

);z;;r lffi ('duU dU = - cosec U* -;

arcts- {

c' = arc"in!+Il.Cul*C.C.C.

8/12/2019 hitung integral

24/33

3+ 'oz

8/12/2019 hitung integral

25/33

fr(TB3Iscas 0 B'TZ:Jz'-TfrNP="1'o.[=+1".

e+zn z B+ xA NP=+nl"r

B+z{l5,,B+2frNP=l"r

n * .,2 ,"ll-.rn

8/12/2019 hitung integral

26/33

*Z"\

rr"

"rBfi + '3.SZ+

_e4

l(. l"t 0 + *l ', '92

-zr\nf"r+

*f ', qoguoc-

rlotuoCuepese;aluad leos-leos ^*(', e)

xp= L* I+ b+'c

/t'e + '3 \, 3_Jt

-xP'-t=

8/12/2019 hitung integral

27/33

"EIZ-=c*!l\=xP t/1e e/r*'3+

8/12/2019 hitung integral

28/33

*t, ,.\

8/12/2019 hitung integral

29/33

5x*3)dx =\rr*'ro*-.1,=T

x+ *2*3*.'*cio*u.! ,, - *)\l?o-=! *LtZ d*-\*t''u* =tr*''',.!,r*+ t6) dx = 3*3 +dx

-Z 5L2*2+5x(*3 * 2)\ *2

8/12/2019 hitung integral

30/33

dx*512*c.

+ a)2 o-=t(e*2+-24x*16x+C.

' ,C.+4, u. =l(x +5- 4*-21 d*=kx+-' lL x+c.e. Illtunglah: ," .t k3 +z)23*2'd*;iul

\2.-dx;( 'c)');{;r}

8/12/2019 hitung integral

31/33

(a*2a*;ta>.xPenyelesalan:Untuk mempermudahpenyelesaian, dlmlsalkar, , *3 + 2 =

U, oaka dffferen- slal

darlU adalah :dU = 3 *2d*.(").((*3*z)2

t*2 d* =(u' )- )( )

4*3 *2ur=+u3 J *.=i,*' J+

8/12/2019 hitung integral

32/33

213+ c-"r.l(*1 ,",.t#+ z)\ *20*=;=tfut u, =3u''2*c=i

I(*3*z>-3.3 *2 d* =i

r*'*z:ttz ru-3 au*c.=i , -r"u-') * c=33*z>2

+c. (x,., .,

8/12/2019 hitung integral

33/33

\/T*2 d* =+\ (*3 +z)-r/4.3*2 d* = +\"-Ll4ilJ-+,u3to)*C=

t_ 9(*3 +

zt3l.4+c.