Page 258 - 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 1 2 2
b
a
- [(log ) − (log ) ]
2
1
- 0@ , ' / @ , &1 0@ , ' 2 @ , &1
2
1 b
- @ , &' ? @ , mÙkj
2 a
mnkgj.k 2- ∫ π/4 tan x sec x dk eku Kkr dhft,A
0

gy % ∫ π /4 tan x sec x ! - [ ]sec x π /4 =   sec π − sec 0  
0 0  4 
- 2 2 mÙkj

3 dx
mnkgj.k 3- ∫ dk eku Kkr dhft,A
1 x
3 dx
∫ - [ 3
gy % 1 x ]log x - @ , ! 2 @ , - @ , ! mÙkj
1
∫ π/2 2
mnkgj.k 4- 0 cos x dk eku Kkr dhft,A

2
∫ π /2 cos x ! - ∫ π  /2 1 + cos 2x  !
gy % 0 0   2  
π / 2
1  sin 2x 
-  x + 
2  2 0 
 sin 2 . π 

1π 2 sin 2 0  × 1 π π
-  + − 0 − = × =  mÙkj
22 2 2   2 2 4


 
∫ π/4 tan x dx dk eku Kkr dhft,A
2
mnkgj.k 5- 0
∫ π /4 tan x dx - ∫ π /4 (sec x − 1) !
2
2
gy % 0 0
π
- [ x ]tan x − π 0 /4 =    tan π 4 − 4 − (tan 0 − 0)   

π
- 2 mÙkj
4
mnkgj.k 6- ∫ a y dk eku Kkr dhft,] tgk¡
2

0

gy % / - & ∴ - & 2
2
2
∴ ∫ 0 a y ! - ∫ 0 a (a − x 2 ) !