Page 264 - 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
∫
- 2 @ , / x !

log x 1  log x +  1
-2 e − - 2  e 
x x  x 
e
∴ ∫ 1 2 log x ! - 2    log x +  e x 1  1  2
2
x
 log 2 + 1   log 1 1  + 
-2  e  −  e  
 2    1  

 1 1 
-2  log 2 + e − 1  0 @ , - 31
 2 2 
 1 1  1
-2  log 2 − e  = 0 2 @ , 1 mÙkj
 2 2  2

∫ π/2 cos x
mnkgj.k 7- 0 (1 + sin ) (2 + sin ) x dk eku Kkr dhft,A
x
gy %

- # j[kdj vkaf'kd fHkUu }kjk gy djus ij


cos xdx
π
/2
∫ 0 (1 + sin ) (2 + sin ) x
log    1 + sin x  sin x       π 0  / 2

x
2 +

 1 
 1 + sin π   1 + sin 0 
- @ ,  2  − log  
  2 + sin 1 π    2 + sin 0 
 2 
 2 
2
1
   3  4
- @ ,  − log  = log   = log mÙkj
3
2
    1   3
 2 
∫ π/2 x
mnkgj.k 8- 0 sin x dk eku Kkr dhft,A
∫ π /2 x sin x ! - x  (cos ) − x π /2 − ∫ π /2 1.( cos ) !
x
−
gy % 0  0  0
- −  x cos x π 0  / 2 +    sin x π 0  / 2
π / 2 π / 2
-2 x   cos x 0  +   sin x 0 

 π π  π 
-2   2 cos 2 − 0 +     sin 2 − sin 0  

- 2 3 /
- mÙkj