Page 247 - 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

Lo&ewY;kadu
uksV

fjDr LFkkuksa dh iwfrZ djsa @@
+ @
E
µ
---------
1- ;fn nksuksa iQyu ,sls gksa fd nksuksa dk gh Kkr gks] rks muesa ls ;fn osQ :i dk dksbZ ,d iQyu
gks] rks mls lnk igyk iQyu ekurs gSaA
---------
2- vko';drkuqlkj lekdyu osQ lw=k dk iz;ksx ,d ls vf/d ckj djuk pkfg,A
---------
3- [kaM'k% lekdyu djus osQ nkSjku iQyuksa osQ pquko dh dksbZ fof/ ugha gSA
---------
4- ,d iQyuksa osQ ;ksx ;k varj dk lekdy mu iQyuksa osQ lekdyksa osQ ;ksx ;k varj osQ gksrk gSA
---------
5- izR;sd cgqin ,d?kkr vkSj xq.ku[kaM fd;s tk ldrs gSaA

14-3 nks ekud lekdy 0!
% &

1- ∫ x 2 1 2 dx dk eku Kkr djuk] tcfd #
− a
1 1
gy % 2 -
2
x − a (x + a ) (x − ) a
1 A B A (x − ) a + B (x + ) a
eku yhft, 2 2 - + -
x − a x + a x − a (x + a ) (x − ) a
∴ 2 & / / & -
⇒ / / 2 & -

nksuksa i{kksa osQ xq.kkadksa dh rqyuk djus ij
/ * 3 rFkk 2 & -

1 1
∴ - vkSj A =−
2a 2a
1 1 1 1  1 1 
∴ 2 2 - 2 + -  − 
x − a 2(ax + ) a 2 (x − a ) a 2a  x − a x + a 
1
1
∴ ∫ x − a 2 dx - 2a    x − 1 a − x + 1 a   ∫  dx
2
1 1 1 1
- ∫ dx − ∫ dx
2a x − a 2a x + a
1 1
- log|x − a |− log|x + a | c+
2a 2a

1 x − a
- log + c
2a x + a
1
1
∫ x − a 2 dx = 2a log x − a + , c x > a
2
x +
a