Calculo Integral
February 20, 2023 | Author: Anonymous | Category: N/A
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ZXGHICN@ MC @ZIAD@DAÔL D@IDSIG AL]CEX@I MCTAES@IM@M CL DGIGNHA@ Q CI ÎLMADC MC EALA
XGDAG OGXCXG À_AI@ BGFL XALDGL DXSR
Zrgocsgr2 _can`r M`laci Xcy D`staiig
SLA_CXTAM@M MC HGEG]À BGXEC ]@MCG IGR@LG D@IDSIG AL]CEX@I HGEG]À 8:01
DGL]CLAMG
MCTAES@IM@M CL DGIGNHA@ Q CI ÎLMADC MC EALA ............................................................................ 4 ZXGDCMANACL]G @L@IÎ]ADG .......................................................................................................... = ZXGDCMANACL]G LSNÁXADG ......................................................................................................... ?
MCTAES@I MCTAE S@IM@M M@M CL DGIGNHA@ DGIGNH A@ Q CI ÎLMAD ÎLMADC C MC EALA
I` ncmam` mc i` mastrahudaôl mc alercsg mc igs f`hat`ltcs mc ul p`îs y su lavci mc mcsaeu`im`m cdglônad` sc pucmc mctcrnal`r ncma`ltc ci îlmadc Eala, lgnhr`mg `sî cl fglgr `i cdglgnast` at`ia`lg Dgrr`mg Eala, quacl ig amcô cl 0108. Ci nátgmg dglsastc d`idui`r cl di`saoad`r tgmgs igsmc fge`rcs mcduyg ul p`îs mc `ducrmg ci alercsg y mcspuás ci pgrdclt`bc fge`rcs alercsg sc` ` igdgl sung ul pgrdclt`bc m`mg mci alercsg tgt`i mci p`îs. Z`r` cstg sc mcoalc ul` ouldaôl mc mastrahudaôl g durv` mc Igrclz (lgnhr`m` `sî cl fglgr `i cdglgnast` cst`mgulamclsc N`x Igrclz) sghrc ci altcrv`ig . Shad`r ul pultg sghrc i` durv` almad`2 ul pgrdclt`bc mc igs fge`rcs quc rcdahcl ` ig nàs ci mci alercsg tgt`i, cs mcdar, quc ci nàs pghrc mc i` pghi`daôl rcdahc sgig ci mci alercsg tgt`i.
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,
>℘()
% %
% %
Lg cxastc ul` òlad` durv` mc Igrclz, sal cnh`reg, tgm`s p`s`l pgr igs pultgs (:, :) y (0, 0) y `mcnàs sgl dôld`v`s f`da` `rrah`. Cl ci d`sg cxtrcng , i` sgdacm`m cs pcrocdt`ncltc aeu`iat`ra`2 ci mc igs nàs pghrcs mc i` pghi`daôl rcdahcl ci mci alercsg tgt`i y `sî tgmg ci nulmg rcdahc ci nasng alercsg. Ci àrc` cltrc ul` durv` mc Igrclz y i` rcdt` namc du`ltg maoacrc i` mastrahudaôl mci alercsg mc ul` aeu`im`m `hsgiut`. Ci îlmadc mc Eala cs ci àrc` cltrc i` durv` mc Igrclz y i` rcdt` , mavamam` pgr ci àrc` h`bg i` rcdt` .
℘()>
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>℘() % >
>
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ZXGDCMANACL ZXGDCM ANACL]G ]G @ @L@I L@IÎ]ADG Î]ADG 0. Mcnucstrcl qu qucc ci îlmadc mc Eal Eala,a, E, cs mgs vcdcs ci àrc` cl cltrc trc i` durv` mc Igrclz y i` rcdt` , cs mcdar,
y>x
> 8 [∘℘()^
Tgiudaôl2
> + >
(
∘ ℘( ℘())
+ > Õℌ > Õ > ( ∘ ℘()) ∫ > 0℘()) 8
8. ·Duài cs ci v`igr mc E p`r` ul` sgdacm`m pcrocdt`ncltc aeu`iat`ra` (tgmg ci nulmg taclc ci nasng alercsg)7 ·Duài cs ci v`igr mc E p`r` ul` sgdacm`m pcrocdt`ncltc tgt`iat`ra` (ul` sgi` pcrsgl` rcdahc tgmgs igs alercsgs)7 Ci v`igr mc E p`r` ul` sgdacm`m pcrocdt`ncltc aeu`iat`ra` cs :.
> [ ∘ ^ > [ ∘ ^
> ∕ >
Ci v`igr mc E p`r` ul` sgdacm`m tgt`iat`ra` cs 0
> ∕
>> ∕
ZXGDCMANACL]G LSNÁXADG Mc `ducrmg dgl igs m`tgs mc i` t`hi` fttps2//mravc.eggeic.dgn/gpcl7am> dgn/gpcl7am>:H43p@XGDnIMGQ0R=RU0yLOk3Q :H43p@XGDnIMGQ0R=RU0yLOk3QVd Vd ) mglmc sc nucstr` (fttps2//mravc.eggeic. igs v`igrcs mc i` durv` mc Igrclz p`r` i` mastrahudaôl mci alercsg cl ci d`sg mc Dgignha` p`r` igs `ðgs 011?, 8:::, 8::=, 8::6, 8:08 y 8:0=2
℘(x)
0. ·Puá pgrdclt`bc mci alercsg tgt`i mc Dgignha` ouc rcdahamg pgr ci 0: % y ci 8: % nàs radg mc i` pghi`daôl cl ci 8:0=7
x :.0:::0 :.8:::0
I(x) :.:0:164 :.:44?06
Zghi`daôl (x) 0:% 8:%
Alercsg (I(x)) 0.:164% 4.4?06%
8. Staiadcl i` rcei` mci pultg ncmag p`r` cstan`r ci îlmadc mc Eala E p`r` ci 8:0= ` p`rtar mc i` altcer`i mcoalam`. Cstan`daôl pultg ncmag. l>3:
∏ > ( ∘ ) > 03:∘ : > 3:0 >:.:8 ()> >(() ∕ ∏ > (00.?06:0) 06:0) ∕:.:8
()>:.8484? > 8 ∕ [ () ∘ ()^
4.
> 8 ∕>8∕:.8?5?= [:.3 ∘ :.848 4?^ >:.34386 Staiadcl EcgEchr` p`r` `bust`r igs m`tgs mc ℘(x) mc i` t`hi` ` ul` ouldaôl
pgialgna`i (alvcstaeuc ci ncbgr grmcl p`r` ci pgialgnag). Er`oaquc igs m`tgs y i` ouldaôl quc rcsuit` mci `bustc. ·Cs ci ngmcig pgialgna`i ul `bustc r`zgl`hic7
Ci ncbgr `bustc dgl igs pultgs m`mg ouc dgl ul pgialgnag mc grmcl 46, cs ul ngmcig r`zgl`hic y` quc sc `bust` mc n`lcr` nuy prcdas`.
=. Sscl ci ngmcig pgialgna`i mc
℘(x) p`r` d`idui`r ci îlmadc mc Eala.
[ ∘ ^
> > ∕ . > .
3. Dgnp`rcl igs rcsuit`mgs ghtclamgs pgr i` rcei` mci pultg ncmag y pgr ci ngmcig pgialgna`i dgl ci m`tg rc`i mci îlmadc mc Eala mc Dgignha` (`ðg 8:0=) rcpgrt`mg rcpgrt`mg pgr ci H`ldg Nulma`i. ·Puá `prgxan`daô `prgxan`daôll cs n nàs às cx`dt`7 XCTSI]@MGT ALMADC MC EALA (8:0=)
H@LDG(HN) NSLMA@I :.385
@BST]C ZGIALGNA@I (@Z) :.34=1
ZSL]G NCMAG (ZN) :.3434
I` `prgxan`daôl nàs dcrd`l` cs ci `bustc pgialgna` pgialgna`i.i.
?. Csdgb`l ulg mc igs mgs nátgmgs (altcer`daôl pgr pultg ncmag g altcer`daôl dgl ci ngmcig `bustc pgialgna`i) p`r`8::=, cstan`r Dgignha` cl igsmc mcnàs `ðgs2 011?, 8:::, 8::6ci yîlmadc 8:08. mc Eala p`r`
8:08
>> ∕[, ∘^ > ,
8::=
[ ∘ ^
> > ∕ , > ,
8::6
> [ ∘ ^ > > ∕, , ,
8:::
[ ∘ ^
> > ∕ , > ,
011?
> [ ∘ ^ > ∕ , > ,
5. Dgnp`rcl igs rcsuit`mgs dgl ci ghtclamg p`r` ci `ðg 8:0=. ·Lgt` `ieul` tclmclda`7 @l`iadc mur`ltc csc tacnpg, du`i f` samg ci pcragmg mc nàs mcsaeu`im`m cdglônad` cl ci p`îs. @ G 011? 8::: 8::= 8::6 8:08 8:0=
ALMADC MC EALA :.3?616 :.36?61 :.3?0 :.3?:81 :.3434= :.34=1
I` tclmclda` mcsmc ci 8::= f` samg ` i` h`b` y ci pcragmg nàs mcsaeu`i f` samg cl ci `ðg 8:::.
6. Ghscrvc y dgnp`rc ci îlmadc mc Eala mc gtrgs p`îscs mc I`talg`nárad` cl igs òitangs `ðgs. ·Duài f` samg ci p`îs nàs mcsaeu`i cl I`talg`nárad` cl i` òitan` mád`m`7
Z@ÎT Hr`sai Fglmur`s Z`l`nà Dgignha` Z`r`eu`y
8:00 :. 381 :.3?8 :.304 :.343 :.384
8:0= :. 303 :.3:= :.3:3 :.385 :.3:5
8:05 :.344 :.3:3 :.=11 :.=15 :.=66
Dgst` Xad` Dfaic Cdu`mgr Hgiava` Zcrò @recltal` Srueu`y
:.=65 :.=5? :.=31 :.=?0 :.==5 :.=84 :.=88
:.=6? :.=3 :.=56 :.=48 :.=0= :.=:0
:.=64 :.=?? :.==5 :.== :.=44 :.=:? :.413
Ci p`îs n`s mcsaeu`i cl igs òitangs `ðgs f` samg Hr`sai, dgl ul îlmadc mc Eala prgncmag mc :.3. Hr`sai cl igs òitangs 4 `ðgs, dgl d gl rcspcdtg ` igs mcnàs p`îscs2
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