Page 257 - DECO403_MATHEMATICS_FOR_ECONOMISTS_HINDI

VED1
E\L-LOVELY-H\math15-1 IInd 21-10-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 VIth 10-9-12

bdkbZ fuf'pr lekdyu

fuf'pr lekdy dk vFkZµtc fdlh iQyu dk lekdy] fdUgha nks fuf'pr lhekvksa osQ fy, Kkr uksV
fd;k tkrk gS rks mls fuf'pr lekdy

, @ dgrs gSaA

∫
;fn f ()xdx - $

rks ∫ b f () ! - [ F ] () x b - $ ' 2 $ &
x
a a
fdlh fuf'pr lekdy

, @ dk eku iw.kZr;k vf}rh;
B gksrk gS] pw¡fd]
∫ f ()xdx - $ / %. rks
;fn

∫ a b f ()xdx - [ F c ] () x + b a - N$ ' / %O 2 N$ & / %O

- $ ' / % 2 $ & 2 % - $ ' 2 $ &

uksV~l fuf'pr lekdy osQ eku ij lekdyu vpj dk dksbZ izHkko ugha iM+rkA

15-1 lekdyu dh lhek,¡ 4

%

la[;k & dks] tks lekdyu fpÉ osQ uhps fy[kh tkrh gS] lekdyu dh fuEu lhek @ & @ rFkk la[;k
' dks] tks lekdyu fpÉ osQ Åij fy[kh tkrh gS] lekdyu dh mPp lhek @ dgrs gSaA

15-2 fuf'pr lekdy Kkr djus dh fof/ $ %

%

fn;s gq, iQyu dk lekdy
, @ Kkr djosQ mls cM+s dks"Bd E esa j[kks rFkk dks"Bd osQ
nkfguh vksj lekdyu dh lhek,¡ fy[kksA vc lekdy esa pj jkf'k osQ LFkku ij mPp lhek j[kdj izkIr iQy
esa ls] mlh lekdy esa fuEu lhek j[kdj izkIr iQy dks ?kVk nksA gy djus ij vHkh"V lekdy Kkr gks tk;sxkA

gy lfgr mnkgj.k

mnkgj.k 1- ∫ b log x dk eku fudkfy,A
a x

∫ b log x ! eku yks @ , - #
gy % a x
1 ! - !#
x
- ∫ tdt
t 2 1 b
- =  (log )  x 2
2 2  a 