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8/3/2019 Anti Derivatives and Area
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Mcea0XXXXXXXXXXXXXX
Cmtgdavg|ctg|as cmd Cvac
[a cva khgmk th cmciwpa c savgas hl soamcvghs th tvw th lgkqva hqt {bct tbasa cvacs {a|a faam
lgmdgmk va~vasamt- Tbaw eqst fa ohmmaotad th davg|ctg|as sheabh{) vgkbt8 Cltav cii) davg|ctg|as
{ava c da~amdamt |cvgcfia dg|gdad fw cm gmda~amdamt |cvgcfia cmd cvac gs c da~amdamt |cvgcfiatgeas cm gmda~amdamt |cvgcfia%gm|avsa h~avctghms- Cish) {a thhj tba igegt cs tbgmks kht gmlgmgtaiw
secii cmd ecmw- Tbct shqmds cm c{lqi iht igja bh{ {a fqgit q~ dgllavamtgctghm-
_oamcvgh 30 Vhss%samsag lgmciiw kht sh lad q~ {gtb shea hl tba bgkb sobhhiavs ~icwgmk gmc~~vh~vgcta
eqsgo cvhqmd bgs lhqvtb cmd lgltb kvcdavs tbct ba ar~ihdad) igtavciiw- Bgs bacd kht sh bht tbct gt
vhojatad q~ gm tba cgv) iac|gmk bgs sbhqidavs fabgmd- [a maad th lgmd bgs bacd cmd vasthva gt th bgs
sbhqidavs sh tbct ba ocm ohmtgmqa tacobgmk- @hm _tagmbcvt) {bh {cs lgrgmk ohe~qtavs ct tba tgea)
ocea q~ {gtb c lqmotghm lhv tba |aihogtw hl Vhss%samsags bacd ct cmw kg|am eheamt gm laat ~av
saohmd0
"c' Tbgmj cfhqt tba lcot tbct |aihogtw gs hv gm htbav {hvds) c obcmka gm ~hsgtghm h|av cobcmka gm tgea- Lgmd tba cmtgdavg|ctg|a hl tba |aihogtw-
"f'[bct dhas tbgs cmtgdavg|ctg|a ehdai8 Gm htbav {hvds) {bct {hqid tba qmgts hm tba r cmd wcras fa8
"o'Kvc~b fhtb tba |aihogtw lqmotghm cmd tba cmtgdavg|ctg|a lqmotghm sgda fw sgda faih{ h|av tbagmtav|ci Z>)3
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"a'Lgmd
kaheatvgociiw-
"k'[bct dhas whqv cms{av eacm8 [bct qmgts {hqid whqv cms{av fa gm8
"b'Ihhj oihsaiw ct tba kvc~b hl tba cmtgdavg|ctg|a- Bh{ ohqid whq bc|a lhqmd tba cms{av whq`qst kht cfh|a fw ihhjgmk ct tba cmtgdavg|ctg|as kvc~b8
_oamcvgh ?0 Mh{) iats saa gl {a ocm kamavcigpa {bct whq|a mhtgoad lhv cmw vcmdhe lqmotghm-
Oiacviw cvac bcs sheatbgmk th dh {gtb tba cmtgdavg|ctg|a- Bavas tba kvc~b hl shea vcmdhe vcta
lqmotghm0
Tbgs lqmotghm va~vasamts tba davg|ctg|a hl shea lqmotghm tbct {a dhmt jmh{- Tbct eacms tbct {a
bc|a cihmk tba |avtgoci crgs- Tba cvac hm tba gmtav|ci Zc) fU gs c~~vhrgectad fw |avw sige
vaotcmkias hl {gdtb cmd hl bagkbt dalgmad fw tba lqmotghm lhv dgllavamt |ciqas hl -
[bam {a iat tba {gdtb hl tba vaotcmkias kat seciiav cmd seciiav th sqaapa gm ehva vaotcmkias)
faoheas -
"c'Iat tba hvgkgmci lqmotghm {a dhmt jmh{ fa c lqmotghm hl w gm taves hl r- _h {a bc|asheatbgmk igja tbgs0 - Tba lqmotghm da~gotad gs cotqciiw tba davg|ctg|a hl tbgs
lqmotghm Ge~igogtiw dgllavamtgcta tbgs lqmotghm- Iat tba davg|ctg|a hl
fa -
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"f'_h mh{ {a bc|a tba aqctghm lhv tba lqmotghm {a|a kvc~bad- Gts
- Th lgmd
tba cvac qmdav tba oqv|a hl tbgs lqmotghm) {a maad th tcja tgmw igttia vaotcmkias hl {gdtb
cmd bagkbt dalgmad fw tba lqmotghm
- Cvac gs {gdtb tgeas bagkbt) sh eqitg~iw
fhtb sgdas hl
fw -
"o' eacms tba obcmka gm hl tba hvgkgmci lqmotghm h|av tba gmtav|ci lvhe r5cth f- Bh{ ocm {a lgmd tbgs obcmka gm w8 "bgmt0 tbgmj cfhqt cm acsgav lqmotghm- Bh{ dh whq
lgmd tba obcmka gm w hl tba lqmotghm h|av tba gmtav|ci Z3)4U-'
"d'_h) jaa~gmk cii tbgs gm egmd) ocm whq taii ea bh{ th lgkqva hqt tba lhiih{gmk gmtakvci qsgmk gtscmtgdavg|ctg|a0
"a'Iats saa gl {a ocm kamavcigpa gt a|am ehva- Iat tba davg|ctg|a hl c lqmotghm fava~vasamtad fw- [a {cmt th lgmd tba cvac qmdavmactb tba oqv|a hl h|av tba
gmtav|ci Zc)fU- Jaa~gmk gm egmd tbct tba cmtgdavg|ctg|a hl gs ) {bct sbhqid tba
lhiih{gmk gmtakvci aqci8
Tbgs gs ociiad tba Lqmdceamtci Tbahvae hl Ocioqiqs "~cvt 3'-