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VED1
E L-LOVELY-H math14-1 IInd 21-10-11 IIIrd 24-1-12 IVth 21-4-12 Vth 10-9-12

fJekJh^14 L :'r (i'V) d/ o{g ftZu nB[ebB

B'N

iK

gfoGkPk Bkb dk d/ ;kg/y nB[ebB j? fJ; soQK d/ ;EkB
f dk oZfynk frnk j?. T[go'es Bshi/ B{z ;ob o{g ftZu do;kT[D d/ bJh f (x) d/ ;EkB

s/ f 1 (x) ns/ d/ ;EkB f 2 (x) oZyD s/

eh s[;hA ikDd/ j' d' cbBK d/ r[DB dk nB[ebB
& gfjbk cbB × d{i/ cbB dk nB[ebB
^[gfjb/ cbB dk fBy/VB r[DKe × d{i/ cbB dk nB[ebB dk nB[bB]

T[go'es fB:w dk gq:'r eoB s'A gfjbK fJj d/y b?Dk ukjhdk j? fe T[go'es fefonk B{z fJZe iK
d' tko eoB s/ nB[ebe iK sK fe;h gqwkfDe nB[ebe dk o{g b? bJ/ iK nfij/ o{g ftZu nk ikJ/
fi;dk nB[ebB gsk ehsk ik ;e/. fJ; ftXh dh ;cbsk pj[s e[ZM nB[ebe d/ gfjb/ ns/ d{i/
cbB d/ nfXnB T[Zs/ fBoGo eodh j?. gfjb/ cbB dh u'D fJ; soQK ehsh iKdh j? fe ;Zi/ gZy d/
d{i/ gd dk nB[ebB ;obskg{oD Yzr Bkb ehsk ik ;e/. fJ; soQK gfjb/ cbB dh u'D ftZu
;ktXkBh posDh ukjhdh j?.
fJ; ftXh d/ gq:'r ftZu e[ZM wjZstg{oD rZbK fJ; soQK jB^
(1) i/eo d' cbBK ftZu'A fJZe cbB nfijk j't/ fi;dk nB[ebB (integral) ;kB{z gsk Bk j't/, sK
T[; cbB B{z jw/PK gfjbk cbB wzBDk ukjhdk j?.
ftZu log x dk nB[ebB n;hA ikDd/. fJ; bJh log x B{z gfjbk cbB wzBDk ukjhdk
j?.

(2) i/eo d'B'A cbB nfij/ j'D fe d'jK dk jh nB[ebB (integral) ;kB{z gsk j't/ sK T[jBK ftZu'A
n
i/eo x d/ o{g dk e'Jh fJZe cbB j't/, sK T[;B{z jw/PK gfjbk cbB wzB'.
T[dkjoD ti'A, ftZu B{z gfjbk cbBk wzBDk ukjhdk j?.

(3) nkfd dk nB[ebB gsk eoB d/ bJh ‘1’ B{z jw/PK d{ik cbB wzB e/
nB[ebB eod/ jB.
fit/A nkfd.

(4) io{os nB[;ko tzfvnk j'fJnk nB[ebB d/ ;{so dk gq:'r fJZe s'A tZX tko eoBk ukjhdk j?.
(5) i/eo ;Zi/ gZy ftZu nB[bB foD fuzBQ d/ Bkb nkgD/ g[okD/ o{g ftZu nk iKdk j? sK ;wheoD
jZb eoB d/ fB:wK dk gq:'r eoe/ gqPB jZb eoB/ ukjhd/ jB.

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