Page 239 - DECO403_MATHEMATICS_FOR_ECONOMISTS_HINDI

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

bdkbZ ;ksx (tksM+) osQ :i esa lekdyu

∫
∫
(3) log x dx , tan − 1 x dx bR;kfn dk lekdy Kkr djus osQ fy, < = dks lnk nwljk iQyu ekudj uksV
lekdyu djrs gSaA
∫
tSls log x dx = ∫ (log ).1 dx bR;kfnA
x
(4) vko';drkuqlkj [k.M'k% lekdyu osQ lw=k dk iz;ksx ,d ls vf/d ckj djuk pkfg,A
(5) ;fn nkfgus i{k esa lekdy ½.k fpÉ osQ lkFk vius iwoZor~ :i esa vk tkrk gS rks lehdj.k gy djus
osQ fu;eksa dk iz;ksx dj iz'u gy djus pkfg,A

uksV~l ge] 'kCn < IJAK= esa] igys vkus okys iQyu dks izFke iQyu o ckn esa vkus okys iQyu
dks f}rh; iQyu pqudj [k.M'k% lekdyu dj ldrs gSaA

tgk¡ L

,
@

izfrykse f=kdks.kferh; iQyuksa

.

bR;kfn osQ fy, gSA

IL I , +

y?kqx.kdh; iQyuksa @ , . @ , ± & bR;kfn osQ fy, gSA
x
JL J@,

chth; iQyuksa (,xx + 1, 2 , x ) osQ fy, gSA

AL A ,
@

f=kdks.kferh; iQyuksa

.

bR;kfn osQ fy, gSA

KL K

@

pj?kkrkadh; iQyuksa & 3 . ! bR;kfn osQ fy, gSA
oSls rks [k.M'k% lekdyu djus osQ nkSjku iQyuksa osQ pquko dh dksbZ izekf.kr fof/ ugha gS] fiQj Hkh fo|kFkhZ
mijksDr fVIi.kh esa of.kZr < IJAK= }kjk iQyuksa dk pquko dj [k.M'k% lekdyu dj ldrs gSaA

gy lfgr mnkgj.k

∫
mnkgj.k 1- log x dx dk eku Kkr dhft,A
e
gy % eku yks ;gk¡ bdkbZ f}rh; iQyu gS D;ksafd ;fn @ , dks nwljk iQyu fy;k tk, rks bldk lekdy

ugha Kkr gks ldrkA
∫ log x dx - ∫ log x .dx
1
e
e
- log x . 1 dx − ∫   ∫ 1 1 dx   ∫ ([k.M'k% lekdyu djus ij)
e
 x 

- log x x − e ∫ 1 x dx = x log x − e ∫ 1 dx
x
- @ , 2 / % mÙkj

x
pkgsa rks ge @ , 2 dks x log Hkh fy[k ldrs gSa] D;ksafd @ , -
e