Page 219 - DECO403_MATHEMATICS_FOR_ECONOMISTS_HINDI

VED1
E\L-LOVELY-H\math13-1 IInd 21-10-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12

bdkbZ lekdyu dh fof/;k¡

izLrkouk
uksV

fdlh iQyu dk lekdyu Kkr djus dh fuEufyf[kr nks eq[; fof/;k¡ gSaµ
1- izfrLFkkiu }kjk lekdyu
,
# "

2- [k.M'k% lekdyu
,
#

13-1 izfrLFkkiu

bl lafØ;k esa fn;s gq, lekdY;
,
dks ekud lw=kksa "
@ esa ifjofrZr djosQ
lekdy fd;k tkrk gSA blosQ fy, lekdY; dh pj jkf'k osQ fdlh iQyu dks vU; pj jkf'k osQ cjkcj j[krs
gSa vkSj lekdY; esa izfrLFkkfir dj lekdY; dks ubZ pj jkf'k osQ iQyu osQ :i esa bl izdkj ifjofrZr dj
ysrs gSa fd lw=kksa dk iz;ksx ljyrk ls fd;k tk losQA

13-2 izfrLFkkiu ls izkIr oqQN ifj.kke "
&
*

iQyu
dk osQ lkis{k lekdyu Kkr dhft,A
gy % eku yhft, & / ' - #
d
dx & / ' - !# ∴ & ! - !#
1
;k ! - !#
a
t
∴ ∫ sin (ax + ) dx - ∫ b (sin ) 1 dt = 1 ∫ sin t dt
a
a
1 1
-2
# / % - 2
& / ' / %
a a

∫ a
b
uksV~l sin (ax + ) dx -2 1
& / ' / %
mi;qZDr mnkgj.k ls fuEufyf[kr iQyuksa osQ osQ lkis{k lekdyu Kkr dj ldrs gSaµ

∫ cos ax dx - sin ax / %
a

∫ sin ax dx *
cos ax / %
a

∫ sec ax dx * tan ax / %
2
a
n
+ )
n
∫ (ax + ) dx - (ax ( an b + 1) + 1 / %
b