Page 279 - DECO403_MATHEMATICS_FOR_ECONOMISTS_HINDI

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

vHkh"V {ks=kiQy ′ gSA Y uksV
L
;fn
{ks=kiQy gks] rks
2a

, 2 ∫ a y dx O a a
0
S X
, 2 ∫ 0 a 4ax dx L

×
, 2 ∫ 0 a 2a 1/ 2 1/ 2 dx = 2 2a 1/ 2 ∫ 0 a x 1/ 2 dx
x

1/ 2 x 3/ 2  a 2.4 a
, 4a   = a 1/ 2 x  3/ 2 
 3/2   0  3  0 
8
2
, a oxZ bdkbZA mÙkj
3

8 2

VkLd ijoy; , $ rFkk ljy js[kk , $ osQ chp dk {ks=kiQy fudkysaA (mÙkj% a oxZ bdkbZ)
3

iz'ukoyh 16-1

y?kq mÙkjh; iz'u

fuEufyf[kr oØksa] v{k vkSj nh gqbZ dksfV;ksa }kjk f?kjs {ks=kiQy dks Kkr dhft,%

1-
- , 4 ls , rdA
2-

- , 4 ls π rdA

∫ 2 π ydx = 2 π x sin x dx =  ∫  − x cosx + sin x 2π
¹laosQr% vHkh"V {ks=kiQy , 0 0 0  [k.M'k%

lekdyu djus ijAº

 8 
3-
1 +  2  , x = 2 ls , 4 rdA
 x 

1 2
4-
5 + x , x = 2 ls , 4 rdA
10

5-
- , ls , rdA
x 2
6-
e , 4 ls , rdA
7- ljy js[kk , 6v{k rFkk dksfV , ! osQ vUrxZr {ks=kiQy Kkr dhft,A