Page 272 - 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 ∞ dx
∫
mnkgj.k 3% 0 (1 + x 22 dk eku Kkr dhft,A
)
b
gy % igys ge - - ∫ 0 (1 + dx 22 dk eku Kkr djsaxsA
x
)
ekuyks -
θ ∴ ! -
θ !θ

vc θ dh lhek,¡ 3.
' gSaA
2
d
- - ∫ 0 tan − 1 b sec θθ = ∫ 0 tan − 1 b cos θ 2 d = θ ∫ 0 tan − 1 b 1 + cos 2θ !θ
4
2
sec θ
 θ sin 2  θ tan − 1 b tan − 1 b 2b
-   2 + 4  0  = 2 + 4(1 + b 2 )

 1 
 tan − 1 b  π π
∴ vHkh"V lekdy - lim  + 2b = + 0 =  mÙkj
b →∞  2 1 + 1  4 4
  b  2 

iz'ukoyh (521

y?kq mÙkjh; iz'u

fuEu lekdyksa dk eku Kkr dhft,µ
dx
∞
dx
∫ 0 a + x 2 ∫ 0 ∞ x 2 a + x 2 ∫ 0 ∞ e − x / 2 !
2
2
x
3) dx
(x +
e dx
∞
∞
∫ 0 ∞ xe − x ! ∫ 0 1 + e 2x ∫ 1 x 6 2 (x + 1)
2
mÙkj
π  2 − 1 
  2  
2a  a 
π 1
π
(58 − 15 )
4 30
Lo&ewY;kadu

2- cgqfodYih; iz'u @ @ + )

µ
a ∫ ∞ f ()xdx dk vFkZ gSµ
6-

& lim a ∫ b f ( )xdx ' lim b ∫ a f ( )xdx
b →∞ b →∞