Page 262 - DECO403_MATHEMATICS_FOR_ECONOMISTS_HINDI

VED1
E\L-LOVELY-H\math15-1 IInd 6-8-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 VIth 10-9-12

vFkZ'kkfL=k;ksa dk xf.kr

uksV
gy lfgr mnkgj.k

3 cos (log x )
mnkgj.k 1- ∫ dk eku Kkr dhft,A
1 x

3 cos (log x )
gy % ∫ eku yks @ , - # rks > ! - !#
1 x

tc - . # - @ , - 3
vkSj tc - !. # - @ , !
3 cos (log )x log 3
∴ ∫ 1 x ! - ∫ 0 cos t !# - [ ]sin t log3
0
-

@ , ! 2

3 -

@ , ! mÙkj

∫
mnkgj.k 2- 1 x dk eku Kkr dhft,A
0
1+ x 2

gy % eku yks -
θQ ∴ ! -
θ !θ
tc - 3. rks
θ - 3 vFkkZr~ θ - 3
1
rFkk tc - . rks
θ - vFkkZr~ θ - π
4

x

∴ ∫ 0 1 1 + x 2 ! - ∫ 0 π /4 1 + tan θ 2
θ !θ
tan θ
- ∫ 0 π /4 tan θ
θ !θ - ∫ 0 π /4 sec θ tan θ !θ

sec θ
- [ ]sec θ π /4 = sec π 2
3 - 2 2 mÙkj
0 4

∫ a x
mnkgj.k 3- 0 a 2 − x 2 dk eku Kkr dhft,A

1
gy % eku yks & 2 - #. rks 2 ! - !# ;k ! - 2 !#

2

vkSj tc - 3. # - & vkSj tc - &. # - & 2 & - 3
x
∫ 0 a a − x 2 ! - 2 1 ∫ a 0 dt t =− 1 a 0 2 ∫ t − 1/ 2 !#
2
2
2
2
1 0
-2  2t 1/ 2 
2  a  2

- 2 03 2 & 1 - & - & mÙkj