Page 246 - DECO403_MATHEMATICS_FOR_ECONOMISTS_HINDI

VED1
E\L-LOVELY-H\math14-1 IInd 6-8-11 IIIrd 24-1-12 IVth 21-4-12 VIth 10-9-12
vFkZ'kkfL=k;ksa dk xf.kr
uksV
% &
: ,d ?kkr xq.ku[k.M
vkaf'kd fHkUu fuEufyf[kr :i osQ gksrs
ckj vk;s gksa vFkok ;fn [k.M
1 1 x 3  − log x x

& x 4 tan − 1 x − − x +  tan − 1 x +  c ' + log + c
4 4   3   1 + x x + 1
− x 2 4 8
cos xx cos ) + tan x + c 8 3 x 3/ 2 [(log ) x 2 − 3 log x + 9 ] + c
x
( sin x +
2
x − 1 x 2 x
! & log (1 + ) x − + + c ' x (log x − 1) log e + c
2 4 2 e 10
x
2[ tan − 1 x − 1 log (1 + x 2 )] + c 1 e x 2 (x − 2 1) + c
2 2
x − cos x log (sec x + tan ) + x c
14-2 vkaf'kd fHkUuksa }kjk lekdyu
ge fl¼ dj pqosQ gaS fd dbZ ,d iQyuksa osQ ;ksx ;k vUrj dk lekdy mu iQyuksa osQ lekdyksa osQ ;ksx ;k
vUrj osQ cjkcj gksrk gSA vr% lekdyu dh ,d egÙoiw.kZ fof/ fn;s gq, iQyuksa dks ;ksx ;k vUrj osQ :i
esa ifjofrZr dj (rksM+dj) mi;qZDr fl¼kar dk iz;ksx djus dh gSA blosQ fy, vkaf'kd fHkUuksa dh fof/;ksa
dk vko';drkuqlkj mi;ksx fd;k tkrk gSA
vkaf'kd fHkUuksa esa Hkax djus dh fof/;ksa dks vki viuh chtxf.kr dh iqLrd esa i<+ pqosQ gSaA
chtxf.kr ls vki tkurs gSa fd izR;sd cgqin osQ ,d?kkr vkSj f}?kkr xq.ku[k.M fd;s tk ldrs gSaaµgks ldrk
gS fd oqQN xq.ku[k.M dbZ ckj vk;saA iQyr% ifjes; fHkUu osQ vkaf'kd fHkUu bl izdkj osQ gksaxsµ
A
gj osQ vuqjko`Ùk
2 & osQ laxr vkaf'kd fHkUu x − a osQ
:i dk gksrk gS] tgk¡ ij ≠ &
izR;sd ckjEckj xq.ku[k.M 2 ' osQ laxr
gSaµ
B 1 + B 2 + ...... + B r
x − b (x − ) b 2 (x − ) b r
;gk¡ ij ≠ 3
Cx + D
/ / osQ [k.M tks ,d ls vf/d ckj u vk;sa laxr vkaf'kd fHkUu osQ :i
x + 2 px + q
dh gksxhA ;gk¡ ij vkSj , nksuksa 'kwU; ugha gks ldrsA
/ / osQ [k.M tks
/ / gS rks muosQ laxr vkaf'kd
Cx + 1 D 1 C x + 2 D 2 C x + r D r
fHkUu + + ...... + osQ :i dh gksxhA
x + 2 px + q (x + 2 px + ) q 2 (x + 2 px + ) q r