7/23/2019 Formulas Calculo Integral (by Carrascal)

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Jhjqhm Bi|akreh)

Bi|akrehaz bilagbiblez)N|mlmz la bi|akrejbi6 SBi|akrehaz binalbe|ez^ SBi|akrehaz la gqijbmiaz

|rbkmimn|rbjez^ SBi|akrehaz la gqijbmiaz btarohbjez^ SBi|akrejbi tmr ter|az^SBi|akrehaz la gqijbmiaz rejbmiehaz^

SBi|akrehaz bntrmtbez^

S g(p" # k(p" ^ lp > g(p" lp # k(p" lp

j g(p" lp > j g(p" lp

Bi|akrehaz binalbe|ez

q > q (p"3 i e zmi jmiz|ei|azJmi q+ za lazbkie he larbwele la q (raztaj|m la p"

E |mlez hez bi|akrehaz za haz laoa eelbr qie jmiz|ei|a la bi|akrejbi (j|a")Zhm bilbjenmz ah bi|akreilm ah razqh|elm la he bi|akreh (gqijbi zq trbnb|bwe")

Ez tmr afanthm he trbnare bi|akreh laoa bi|artra|erza6

q+ qi lp > S qi#5 - (i#5" ^ # j|a (zbantra uqa i .5"

Kaiareh Jezm ter|bjqher (q > p"

Bi|akreilm _azqh|elm la he bi|akreh Bi|akreilm _azqh|elm la he bi|akreh

q+ qi (zbantra uqa i .5" qi#5 - (i#5" pi pi#5 - (i#5"

q+ - q hi q 5 - p hi p

q+ eq eq - hi e ep ep - hi eq+ aq aq ap ap

q+ - (5 # q?" erj |k q 5 - (5 # p?" erj |k p

q+ - (5 . q?" erk |k` q 5 - (5 . p?" erk |k` p

q+ - (5 . q?"5-? erj zai q 5 - (5 . p?"5-? erj zai p

q+ - (5 # q?"5-? erk zai` q 5 - (5 # p?"5-? erk zai` p

q+ jmz q zai q jmz p zai p

q+ zai q . jmz q zai p . jmz pq+ - jmz? q |k q 5 - jmz? p |k p

Bi|akrehaz la gqijbmiaz |rbkmimn|rbjez

Jmizblaranmz he bi|akreh6 _ (zai p jmz p" lp

Zb _ (zai p jmz p" az bnter ai zai p3 _ (. zai p jmz p" > . _ (zai p jmz p"

jmz p > | zai p > (5. |?"5-? lp > . l| - (5 . |?"5-?

Zb _ (zai p jmz p" az bnter ai jmz p3 _ (zai p . jmz p" > . _ (zai p jmz p"

zai p > | jmz p > (5. |?"5-? lp > l| - (5 . |?"5-?

Zb _ (zai p jmz p" az ter ai zai p jmz p3 _ (. zai p . jmz p" > _ (zai p jmz p"

|k p > | zai p > | - (5 # |?"5-? jmz p > 5 - (5 # |?"5-? lp > l| - (5 # |?"

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Zqz|b|qjbi kaiareh

|k (p-?" > | zai p > ? | - (5 # |?" jmz p > (5 . |?" - (5 # |?" lp > ? l| - (5 # |?"

Jmizblaranmz he bi|akreh6 zain p jmzi p lp(n -m i tqalai zar tmzb|bwmz m iake|bwmz"

Zb n az bnter Za eja ah jenobm jmz p > |

Zb i az bnter Za eja ah jenobm zai p > |

Zb n i |baia bkqeh terblel Za eja ah jenobm |k p > |

Bi|akrejbi tmr lazjmntmzbjbi (tere gqijbmiaz |rbkmimn|rbjez"

zai np jmz ip lp > Szai (np # ip" # zai (np . ip"^ lp

jmz np jmz ip lp > Sjmz (np # ip" # jmz (np . ip"^ lp

zai np zai ip lp > Sjmz (np . ip" . jmz (np # ip"^ lp

M|rmz jenobmz

zai? p > (5 . jmz ?p" jmz? p > (5 # jmz ?p"

Bi|akrehaz la gqijbmiaz `btarohbjez

Jmizblaranmz he bi|akreh6 _ (zai` p jmz` p" lp

Zb _ (zai` p jmz` p" az bnter ai zai` p3 _ (. zai` p jmz` p" > . _ (zai` p jmz` p"

jmz` p > | zai` p > (|? . 5"5-? lp > l| - (|? . 5"5-?

Zb _ (zai` p jmz` p" az bnter ai jmz` p3 _ (zai` p . jmz` p" > . _ (zai` p jmz` p"

zai` p > | jmz` p > (5 # |?"5-? lp > l| - (5 # |?"5-?

Zb _ (zai` p jmz` p" az ter ai zai` p jmz` p3 _ (. zai` p . jmz` p" > _ (zai` p jmz` p"

|k` p > | zai` p > | - (5 . |?"5-? jmz` p > 5 - (5 . |?"5-? lp > l| - (5 . |?"

Zqz|b|qjbi kaiareh

|k` (p-?" > | zai` p > ? | - (5 . |?" jmz` p > (5 # |?" - (5 . |?" lp > ? l| - (5 . |?"

Bi|akrejbi tmr lazjmntmzbjbi (tere gqijbmiaz `btarohbjez"

zai` np jmz` ip lp > Szai` (np # ip" # zai` (np . ip"^ lp

jmz` np jmz` ip lp > Sjmz` (np # ip" # jmz` (np . ip"^ lpzai` np zai` ip lp > Sjmz` (np # ip" . jmz` (np . ip"^ lp

M|rmz jenobmz

zai`? p > (5 # jmz` ?p" jmz`? p > (jmz` ?p . 5"

Bi|akrejbi tmr ter|az

q l w > q w . w lq

_akhe inm|jibje tere rajmrler he grnqhe ei|arbmr6 Qile w qi wbafm zmhlelm waz|blm la qibgmrna

Bi|akrehaz la gqijbmiaz rejbmiehaz(jmjbai|a la lmz tmhbimnbmz"

5) Zb ah krelm lah iqnarelmr Za `eja ah jmjbai|a za ethbje he rakhe lah jmjbai|a

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az nemr m bkqeh uqa ah krelmlah laimnbielmr

L > l J # _ >>9 L - l > J # _ - llmila L az ah lbwblailm l ah lbwbzmr J ah jmjbai|a _ ah raz|m)

?) Zb ah krelm lah iqnarelmraz naimr uqa ah krelm lahlaimnbielmr

Mo|aianmz hez rejaz lah laimnbielmr lazjmntmilranmz ah bi|akreilmai grejjbmiaz zbnthaz zaki jmnm zaei lbj`ez rejaz)Hmz jmagbjbai|az la hez grejjbmiaz zbnthaz za mo|baiai lazerrmhheilm hmz

tmhbimnbmz a bkqeheilm jmagbjbai|az e enomz helmz m leilm wehmraz/ez|q|mz/ e he p (trajbzenai|a hez rejaz lah laimnbielmr" m anthaeilmenomz n|mlmz)

?)5) _ejaz lah laimnbielmrraehaz lbz|bi|ez

5 - (p.5" > E - (p.5" # O - (p#5"

?)?) _ejaz lah laimnbielmrraehaz nh|bthaz

p - (p.5" > E - (p.5" # O - (p.5"

?):) _ejaz lah laimnbielmrraehaz lbz|bi|ez nh|bthaz

(navjhe la ?)5 ?)?"

5 - Sp (p.5"^ > E - p # O - (p.5" # J - (p.5"

?) j # p |

Zb e p? # op # j > e (p." (p. "

Za `eja ah jenobm (e p? # op # j"5-? > (p." | zbailm (p." qie la hez lmzrejaz raehaz la e p? # op # j

_ (p (.e p? # j"5-?" lp p > (j - e"5-? zai | p > (j - e"5-? zaj` |

_ (p (e p? . j"5-?" lp p > (j - e"5-? zaj | p > (j - e"5-? jmz` |

_ (p (e p? # j"5-?" lp p > (j - e"5-? |k | p > (j - e"5-? zai` |

Bi|akrehaz obinbjez Zmi la he gmrne pn (e # o pi"t lp

Zb t az qi inarm ai|arm Za lazerrmhhe tmr ah Obimnbm la Ia{|mi

7/23/2019 Formulas Calculo Integral (by Carrascal)

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tmzb|bwm

Zb t az qi inarm ai|armiake|bwm

Za `eja ah jenobm p > | lmila az ah nibnm jmni nh|bthm la hmzlaimnbielmraz la n i

Zb t az grejjbmierbm (la hegmrne r-z"

Za jehjqhe (n#5"-i). Zb az ai|arm za `eja ah jenobm6 e # o pi > |z. Zb az grejjbmierbm za jehjqhe6 t # (n#5"-i) Zb az|e jei|blel az ai|are za`eja ah jenobm e # o pi > pi |z

Bi|akrehaz bntrmtbez

La trbnareaztajba

Jqeilm |baia bigbib|m zq bi|arwehm la bi|akrejbi)Jrb|arbm lah hnb|aJehjqhenmz (jqeilm p |baila e" hbn g(p" pe> c gbib|m (tqala zar jarm" jmi e 9 5 >>9 he bi|akreh az jmiwarkai|albz|bi|m la jarm (tqala zar" jmi e 5 >>9 he bi|akreh az lbwarkai|a

Az jmilbjbi iajazerbe uqa hbn (jqeilm p |baila e" g(p" > 4

La zakqileaztajba

Jqeilm ah bi|akreilm im az| ejm|elm ai ehki tqi|m lah bi|arwehm la bi|akrejbi.Zb ah hnb|a zqtarbmr (o" az ah uqa za `eja jehjqhenmz hbn (jqeilm p |baila eo."g(p" - (5-(o.p"n" > H.Zb ah hnb|a bigarbmr (e" az ah uqa za `eja jehjqhenmz hbn (jqeilm p |baila ee#" g(p"- (5-(p.e"n" > HZb H az qi inarm gbib|m (tqala zar 4" jmi n 8 5 >>9 he bi|akreh az jmiwarkai|aZb H az lbz|bi|m la 4 (tqala zar" jmi n 5 >>9 he bi|akreh az lbwarkai|a

Tkbie bibjbeh (ei|az ai ||t6--az)kamjb|baz)jmn-gbzbjez"6 `||t6--{{{)jerrezjeh)ia|