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VED1
E\L-LOVELY-H\math16-1 IInd 21-10-11 IVth 21-4-12 Vth 20-8-12 Vth 20-8-12 VIth 10-9-12
bdkbZ lekdyu osQ vkfFkZd iz;ksx
uksV
∫ b f
uksV~l a ()xdx og lEiw.kZ {ks=kiQy gS tks oØ , - 6v{k vkSj , ls , lhekvksa
osQ vUnj curk gSA
oØ , - 6v{k rFkk js[kkvksa , vkSj , ls f?kjs {ks=k
dk {ks=kiQy fuEu lw=k ls
Kkr fd;k tkrk gS%
x =
, ∫ x = a b y dx
ck;ha vksj osQ fljs ij dk eku , lekdyu dh Y
fuEu lhek rFkk nk;ha vksj osQ fljs ij dk eku ,
f x)
lekdyu dh mPp lhek ekuh tkrh gSA A y =( B
blh izdkj oØ , - 6v{k rFkk js[kkvksa , rFkk
a b
, ls f?kjs {ks=k dk {ks=kiQy fuEu lw=k ls Kkr fd;k tkrk gSµ = =
x x
y =
, ∫ y = a b x dy O D C X
bl n'kk esa lekdyu dh lhek,¡ uhps ls Åij dks yh tkrh gSaA
gy lfgr mnkgj.k
mnkgj.k 1- v{k ,oa dksfV
osQ chp dk {ks=kiQy Kkr dhft,A
gy % fn;s gq, oozQ dk lehdj.k
,
lehdj.k (1) esa , 4 j[kus ij , 4 ∴ 6v{k ij , 4
∴ vHkh"V {ks=kiQy , ∫ 0 2 ydx = ∫ 0 2 mx dx = m ∫ 0 2 x dx
x 2 2 m
, m = (4 − 0) = 2m oxZ bdkbZA mÙkj
2 0 2
mnkgj.k 2- ijoy;
rFkk ljy js[kk
osQ chp dk {ks=kiQy Kkr dhft,A
gy % ijoy; dk lehdj.k
, $
js[kk , $ ijoy; ls
rFkk ij feyrh gSA
vHkh"V {ks=kiQy
gSA
