integrales definidas2

15
tO{- tn{* tu{+ rr+9{ =[r-.,) {- ¡r+r){l *t f\octdo'rratzl gvqard".¡d1 ("t[- 1r+*? { - CO{+ (r+.1{" fr,-lr{ * (r4tt l]-? (v>rdo>i"l2l gesl,rdos|) (r-*J{ - t+f s Ir-!]d-(rUl:l (1 (o t:, (1 (v ('' (e, { -tq{ = Lr'-nj-rx{l? ( r,,.,'rnq,{{.'ie sosardo{d ) rdf + ,,lf ?t : f t}r8i (t?{13 (€ t.r.ug+too) sa XttD{ X = (t)-J' X? -.1 -u (? r+ub+9uo ) r^ 't tB I 'xrxq=tá (? | anur?¡<tro) S, X rN(t+r4^-u) = ): (, (l 'SüllororuAs rq jag.ofatdo.r¿ ? s-r , ?-.! .i +"h+¿t + ,2.).7 = n))= .l= rlJ ¡l role '^ra(? {od Jorrg¿oS arrr^rt1 l? €a + U .tott"¿bl ,{l@ll l" 5a <f- t,^l ál.l er.(e4 o 2 r lpul \? l" I ,! .rr*o¡f'*n5 "g o\o10lt (p\^6lf "i ¡- 3 ru¡J +'"' *(ü+.^a1{ r (r+Ll{* C+l = eJz ú os2 eLea I tulj ".'((r+w)d r f*ú ,ourw{elSe1 ap low¡5 so1 \o_Lt?6?¡¿a,l q"! r)tlF oloi'atts la 'U5)5t^¡ t¡o? /?\-eo, oto¿ rrgrurdaf uorrunJ oun !k ,.¡r? q anG s?p! ,orr.uo so{rqo\^ sot uG'r^¡ .a?5 5 VlJo¡v\^rO 5

Upload: franklin-yungure

Post on 05-Nov-2015

249 views

Category:

Documents


0 download

DESCRIPTION

INTEGRAL DEFINIDA PDF

TRANSCRIPT

  • tO{- tn{* tu{+ rr+9{ =[r-. ,) {- r+r){ l * t

    f \octdo'rratzl gvqard".d1 ("t[- 1r+*? { - CO{+ (r+.1{" fr,- lr{ * (r4tt l ]-?

    (v>rdo>i" l2 l gesl , rdos|) ( r -*J{ -

    t+f s I r - ! ]d-(rUl : l

    (1(o t : ,(1

    (v (''

    (e, { -tq{ = Lr'-nj-rx{l?

    ( r,,., 'rnq,{{.' ie sosardo{d ) rdf + ,,lf ?t : f t}r8i (t?{13

    (

    t . r .ug+too) sa XttD{

    X = ( t ) -J ' X?-.1 -u (?

    r+ub+9uo ) r^ ' t tB I

    'xrxq=t (? |anur?

  • tol{- rn{* ,ul{+ (r+9{ =&,-, , {- rrr){ l *3'

    Cctdqrratal gvqard" ' d ) (" tS- (r+*? { - C{+ ( , ru1{. f t , - l r { * t r+t l l l -?

    (u>rdo>52121 gescrdos|) U--J{ - t+f s [ , - t ] l - ( rU]: i

    (1(" ( : ,

    (1

    (v (*'

    (e,{- tq{=lr tJ-rrr{ l?

    ( .,, ',."nq,{{s1e sosardord ) fdf t ,,lJ ?t : f {lr8-* (J?{l:

    (

    rug+roo? sa X(D{ I= ( t ) { 'X?-.1 -rl

    't'ot&rowas "q

    jae.'gatdo.r

    ? ! , ?-

  • kf l i , ,nu)] * l

    f1r*ul n \ . : . r , , t to ut

    t l+u?ul+ l r t r l+"""+ 6Ul* .r tlttur ?U

    oqVet\ drns" q

    -- '. ' t o l? \oS

    1rl ?vl t a l \2Q

    oldwaC 3

    =i| (=u

    r* l3u

    ,rr1616 t ( rc) ua Srogoo 6l

    ( q ( t+ u) lu l = qtu

    g.og>rd.t v :od r 6tual tod(r( t -J)=.(r- t l { 6

    h="( l - l l - ( t+ l ) oa'o)

    t : !

    Io l , - l ) - r r '+Pl l

    fo

    : ?u"r+ >l e6)ozsaqa

    l (

    "(r+)-- ( r+,r7 l "2to+u r l . ( i l i rs

    :T'GTl r l

    (r *0 -rf '

    " l)] ? cvd vlora;"roJ rouo ? \o

    " \ 'o?

    ! olct''ra(

    o,. l f stq.J :Ef gPlcj t

  • .o ? )d\c- E 'rc1 o(oq ,orta rgob.ol t { .a(a p

    5o-a* Sol { tO,/ , "on{o) olrocl -opcr-rw1\ ucrOlJ 0ftd tOn

    1- u4 ) " . . > lX >=.s ga1'ot f .rx(""(1r( ' -- rxiex 3 rd o{u^Gur 1,

    oltonlagl laf urol2r.r- - rvd vu log-qa7 O\en r f lut l , n [q

    oPeJlr2 q194r1u\ u 3( ' ( )yl"rdl 's

    "v rn$rg ra\

    t (Qw+so\ r@ "t J at

    B 1tx ( v sx gapzr.r . raf i

    trror6a{ -ol a 5' [1 ( roJ ? X A(rB s A / U1 aS? uF " XV s I tCJl l rXV s X lV

    Saeott)a f "o1crG-:r1 ]orc-rcd 'arQ l2r^r.o-)l ?5 t"t(-] aq Uror>1.t*.cod 1a1

    ' += XV Sa o\r,rr+ur9as -og-w7 aq gn-u$vol vrl( g.+r$ro\

    rvr4rgtr^r v1 "u2r+ "" ,Q

    So\\on.\Lur loS U " "QlArQ 25 [q(O] opA?rul F oQao?

    f( , r - . ' ( t* ' t lXlVJ f .wt, l ' t1d oJ?wnu Y u,o.r)r{{r l , \?Q r lqrsot \ " - ,11 " t

    (tr(s

    'v-g=XWt2 ant erdr- t f1 2f ' r^ f" ' l l (( l , lA

    t-)X* l( -

    y,1g rod v')rqut "t l f X' l f Xl o\onr>{ul lc\S eQs? "t po*rGuo1 wl G

    {"fxe r 'sKl ( ' " ' '

    L '* ' ,x l r [ x ' .x1 ] I 5a o+r?

    Lqtr l ] opn{e.r ,\ \v 5o1'rrA1t{nf u \ : "Q1\\ \ [Ct.o]

    at d uoot2r\rro

    { t"J 0C.

  • 'o loJ){ot9nS o,^arte ^} l t , " o? olnGuuo?-q Un"e \paAt

    ?0 -(? plg) r^t l L\1os..dra a",9 ec\$ x v c lh? J 6-- .g. ld \a raoro$ ,5nt(.o,(6r l

    * , rp, lv-ror9 ?0sa{o.plun (}n)J ha(1ep

    "Q t"(fruY-) xtV va? oun ofe? r501n6uxar"J>.t \ lOrntt,-r5tlo) v{o\v

    ' lXfr-r .1 1ua,J"g orr ' tosq\] @q,r \ tv1^/ . ro, tp\ \? Sa ( lAf 5q @{nloSl l : owrrulvl {o\nq F se ( lh) J "q, y\ f t f r r - t ,X I

    "

    t { r q

    ut ts)x7 (o. . rar+xa leyf \ \ "6 l \oura16r2 \ t , "d o Ulo ' ' t6( 1 =? N( I ,Xt t - \ tolo0 l {11l \pg.o) l r ? raouir .os: tn ) S r) uolva f l { { ua oul lUo? r , J ou ol

    ' ( r" ' r6t1=)f t I ( t - ix)- s )r \e sa Q.r \G,Jo\ nR.cqwt5' ,?

    - l a s: Lf X(- f l aquot f r ( . "1 .q uorr r -sv,d -ou\ !u r . "" 1

    olv J>t! \ 1c\ 5

    rX(o l s ots

    ?-l )---',

    )+---=',

    vte44,=

    4

    :--r--l_*:*-+__-*--+----a--=-+--'--------__L-

    !----

    T"

    ---+*--f-

    ..-.-.-1-

    ---_-*-

    "-T-

  • xq ()4 )! .1)7

    \.)< {q ( , r ru J +"" + Xv (a&) i* xq [ ,4.J = S

    red

    o\h

    'rod oq"g +i:sa

    Se)$o\Oa I

    5d+ t-(" t \ ,1u

    ffi 'xv

    oqae nsa Ja.ltr?9--nJrl? SqoQ.ro+cal \ soP\ P++ vasv 1aQ sgq"\I

    = W (urt l j +"" .+ Kq(vr l J+ (s l f r t1J s \z

    u

    So1",Guo;.a{ SQ\fq lv.+ roaso yO q}q2u\ -o\q.rG.r.\ vq^

  • - (+ol" i+^ rq tr )

    co(- \J

    - t l < Jts4

    so;rJr . ,sQ so1:r)

    Xv (:r) J vIs]d7,t

    r '?7u

    .lscJ avlJ?Q 2 5 tl( v] ut J "t

    o(.gE U uorQa,r art \a2la l"e y?ele2L/ ol I Szr,ro+U)

    g\c ' r I

    I "?

    =(j\

    atrar1-?S 0 o1o-w

  • [ 'Gtg ]

    /'7t1"2

    *

    ,{ , - QQI - ' * J /

    .1 ?t 'WV -un{ ior!

    e-o-?rr s(* - # ?tL)

    * ;1 = (* - utG

    - n2-v

    Itr-

    ?t =

    ' Qac-v0rJ *1 \ .3

    ( t ,* ' ' ' * ,

    (6,*ru ' , ( l+ rr)

    L\iL)L) ZZ - # :u-*0,) * : l i 3

    1 ooG L'l* 88f J

    - , \ =

    zIF-a

    - . t+u7

    (,-1-:_yn

  • 'AU??1+ At. Ou? fuuat>o+t+.sots

    G 6"0* lcloJd

    a+sl*a en$ zrduua5 xqer i l ; [ - = x l tner $' . ( , rJ:\

    rf (rrlY'(t\

    ! arxaf,1fvJ

    oe ctq eu, a t) -.aoytt67-tu1 52 J tsa o+S>

    lsauauva [q9 "- vogr1uG> a ) t ,$ : Vqt?{oal

    "retxa euwr[ a+s t5 (

    x ]V ( ls ) J '4 t t - g{ [ . r ^ f

    L,oJ o\ = I 0" , i t \ v . r

    i e,^ro2 autJ)? "5

    t * \ tx?J v ' \

    s fou

    -rod wgol- ,* t l ' 1v p a{ , j a8 (uoqret l ) .aplotruua(, lo.r?larulnl teJva+rn ( 8q xa] ogv--r . la2 olv ta+t) \ t ) ( ' ) L la f lptvtAf uettuoJ oun J nU5

    fr uP J vrotcvo

    1os,b-zlul t I

    'oawou g Sa i1 v

    nprurJaCJ,

    ol a? -@qlurJef 1 'os2ful v

  • [ , r - , .+ ({+\u?l-t Qo+-u

    -8h - 6frc- I , t \lr . rf i - 6,

    Qf

  • = )\ l r .ot- o0l) { l ) )U,)a 2A5 bo) U)I oo

    ool (- LJ

    -t \

    ?tGs Q*o- 'J i ' : t - :

    f* u u - l t+c-uLc-T-1--st- t -oht l t r , l { l =i*- ft-,,4

  • ^ t t ' 'r"t\f? 2 oc+oz t

    ru- r\1o"

    -1,ot , l 5 - t , r$; [s?)oo: ' t f "X f t .

    oq turg C t l l .q ** Iur aqlnrtar,ur l> { ,S 'S

    x1r 'd ' (*nr,"{n( " [u1,J u ""$ *(n" i r \

    ,?ua!.1. ,s Q frrv] . 5ua pr l . , - ,saLui r : { t rro. i -p?'L*t4q t t f

    -q 4a1.,^. . !2+ul sql u2 a\ l .oselut sa j 15 , h

    -

    nr ,Y( ' ar*\ (sq

    1)+ x\ ts{=

    " tL,{ ,G{qlr \

    {( r$ i} \ , = -qN1 \1v 1u

    l-,,*.[ |Qi^ul radrs

    'g

    [= e f ,1 olv/.. j,r\,u\q*5

    .r- r11-".Qr*Ut < ) S?) u6'+u? /!0, ,*eoGr*Ul .,oraUl! V]^ SA J ,S ,l

    s

    \(cluld"Q 1'"

  • 'k/ t= loto-frs ' ) ) - : L^ ca: I -

    *-

    'l + = fftl - t= f -JG+a lao U I Luo> YorTvn[

    .owa4o l - op u. ,9a 5 ) "

    . (

    'tl*er p I A r c,gf = \:t,rrn lJ.,1ri q (q?)f rr . vo,?onJ vur) t? { tS

    lr",Lue e.r?(.roJ ?@ r

  • "il

    fs,zut

    '1, , *T

    h s ott , ; \

    il r- t ,Gurr I ,,rJ" ,

    qt

    =@.,1

    z t, l

    6eE+|? vtJ

    " ,

    ; [ :s\

    \(/ , " \ sf'/t\

    3I

    ' g9u-.x l9

    -5 ,--5-\o3r

    I

    -

    ;\

    *r ( ry) , , ;5' * t

    ora L"Jof 6o Gr*r 7 r ,

    Sa>uo'-ra t=CoF

    [.- [qfr :g nqr.p

    \ol -cr{'- d h/t a- aS lS

    @"225 o(r o ( @d"s ' Ca-FF|-JT]

    ," \

    zX-i or/ ( @,Trq \ r l (v

    :or1d*a(9

    " f r r tq"((+){1= -( .* : \

    q\ .o= (e: G ]Ju,

    ' fOn "r y?.ur lut -oro.r** au., \JF

    '(trS = l-r,'aq, .-: (rl9 .od \o*Q-rut '\ -( X a\olr?r-{Y{\

    q Lq

    ( .o1 s\ \ r - r?or!us) eor)aJ'oc\ e? { tS: owareaf

    \pt lu>'t lerQalu\ -\ouq \r-P ?1\ 'o r us -

    e 6t l- l^r-r 'J

  • r - L l6 :e) l -*/o' 7.*Lu! l .s ( ! ' t :Z

    t ' [ r Ii - l "* ' , r l ; f(_! .J

    . ' \PJ\ l

    I oPc'r ' r"1st l I^ l

    lPI

    t r ' l t

    l ,n iF (r , tL-- ' l \r i

    {J- .

    Yf *r = 11.\

    x1 x \"v

    / - .1\t - t . r lE, l t r Kf 5.

    ' I \

    f*