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VED1
E\L-LOVELY-H\math16-1 IInd 6-8-11 IVth 21-4-12 Vth 20-8-12 Vth 20-8-12 VIth 10-9-12

vFkZ'kkfL=k;ksa dk xf.kr

uksV 4
vr% {ks=kiQy , 2 ∫ 0 y dx
1 A
4
4
2
, 2 ∫ 0 4x dx = 4 ∫ 0 x dx
 2 3  4 O x
, 4 ×  x  2
  3  0 

8  3  B
, 4  2 − 0
3    

8 64
, (8 − 0) = oxZ bdkbZA mÙkj
3 3
x 2 y 2
mnkgj.k 3- nh?kZo`Ùk +

dk {ks=kiQy Kkr dhft,A
a 2 b 2

gy % nh?kZo`Ùk

′ ′ dk {ks=kiQy Kkr djuk gSA ge igys {ks=k
dk {ks=kiQy Kkr djsaxs vkSj
pkSxquk djus ij vHkh"V {ks=kiQy Kkr gks tk;sxkA
Y
x 2 y 2
+ , B (0, )b
a 2 b 2
y a
 x  2 (, 0)
∴ , 1 − 2   A O dx A X



 a 
b B
2
⇒ , a − x 2
a
fcUnq osQ fy, , 4 vkSj
osQ fy, , 4 j[kus ij] fcUnq o
osQ funsZ'kkad Øe'k% -
o - 4 gksaxsA
∴ vHkh"V {ks=kiQy , 4 ∫ 0 a y dx

b
a
2
2
, 4 ∫ 0 a a − x dx
bx 1 1 x  a

, 4  a − 2 x + 2 a 2 sin −  = π ab oxZ bdkbZA
a  2 2 a 0 
mÙkj

mnkgj.k 4- ijoy;
vkSj bldh ukfHkyEc thok ls f?kjs {ks=k dk {ks=kiQy Kkr dhft,A
gy % ijoy; dk lehdj.k
, $

rFkk ukfHkyEc thok dk lehdj.k ,

ukfHkyEc thok ijoy; ls vkSj ′ fcUnqvksa ij feyrh gSA