Page 260 - 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 2
mnkgj.k 10- ∫ x log x dk eku Kkr dhft,A
1
gy % [k.M'k% lekdyu }kjk

∫ 1 2 x log x ! -    x 2 2 log x     2 1  2 ∫ 1 2 1 x 2 2 !
.
x
 x 2  2 1 2
-  log x  2 ∫ x dx
 2   1  2 1

 x 2  2 1 x   2 2
-  log x  2  
 2   1  2  2   1 
1 2
- @ , 2 x   2 
4 1 
1
- @ , 2 0$ 2 1
4
3
- @ , 2 mÙkj
4

∫ π /4
mnkgj.k 11- 0 tan x dk eku Kkr dhft,A

∫ π/4 tan x ! - [ π / 4
gy % 0 ]log sec x 0
π
- @ ,
@ ,
3
4
- @ , 2 2 @ , . 0 @ , - 31

- @ , 2 mÙkj

mnkgj.k 12- ∫ 0 π/6 1- sin 2x dk eku Kkr dhft,A

gy % ∫ π /6 1 − sin 2x ! - ∫ π /6 cos x + 2 sin x − 2 2 sin x cos x !
0 0

2
- ∫ π /6 (cos x − sin ) !
x
0
- ∫ π /6 (cos x − sin )xdx - [ cos x ]sin x + π / 6
0 0
π  π 
- sin 6 + cos 6   2 0

3 /
31


 1 3  1 3
-   +   2 3 / - + 2
 2 2  2 2

1 + 3 − 2 3 − 1
- - mÙkj
2 2