Page 282 - DECO403_MATHEMATICS_FOR_ECONOMISTS_HINDI

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

D;k vki tkurs gSa miHkksDrk cpr
{ks=kiQy {ks=kiQy
x
, (ek¡x oØ) 2
∫ 0

mnkgj.k 3- ekuk dksbZ ek¡x oØ

gks vkSj bdkbZ gks rks miHkksDrk
cpr fudkfy;sA

gy % ;gk¡ ek¡x oØ] , 44 2 ' 0 ! gS rFkk ek¡x dh ek=kk , ' gS rks ;gk¡
, 44 2 ' 9 ! 0 ! 9 ' 9 ' , 44 2 <4 , 4

miHkksDrk cpr , 0 ∫ x (ek¡x oØ) 2

, 0 ∫ 3 (100 − 5x + 3x 2 ) dx − (p × 3)

 5x 2 3x  3 3
, 100x −  +  − 30
 2 3   0 

5
, 44 9 ! 2 ! 9 ! 0 ! 9 ! 9 ! 2 !4
2
, !44 2 ' 0 ; 2 !4 , ;$ '

mnkgj.k 4- ek¡x iQyu%

gS] ;fn

gks rks miHkksDrk cpr D;k gksxh\
gy % ek¡x iQyu_ , '4 2 ' 2
;fn , 4 gks rks
4 , '4 2 ' 2

vFkok 0 ' 2 '4 , 4

0 4 2 ' 2 '4 , 4
;k 2 4 2 ' 0 4 , 4
;k 2 ' 0 4 , 4
2 ' , 4 ;k , '1 blh izdkj 0 4 , 4 ;k , 2 4

;fn ge , 2 4 dks NksM+ nsa D;ksa 3 4] vr%

miHkksDrk cpr , ∫ 2 5 (50 − 5x + x 2 ) dx − p × x

, ∫ 0 5 −(50 + 5x x 2 − ) dx × 0 5

 5x 2 x  3 5
, 50x − − 
 2 3   0 
 55 5  × ×
×
, 50 5 − 5 5 5 
×
×

 3 