Page 209 - DECO403_MATHEMATICS_FOR_ECONOMISTS_HINDI

VED1
E\L-LOVELY-H\math12-1 IInd 21-10-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 VIth 10-9-12

bdkbZ lekdyu % lekdyu osQ vk/kjHkwr fu;e

− 1 1 uksV

! & / % ' @ , / / % % 2x + c ! / %
2
x
2 x 3 x b x b x + a
$ & + c ' + c % + c ! + c
log e 2 log e 3 log e b log e b

' &

# / % '
( / % %
/ % ! ) %

* &
# / % ' 2 ( / % % 2
/ % ! 2 / %
5 x
7 & 2
/ % '
/ % % log 5 + c !

/ %
e

12-4 fdlh vpj vkSj ,d iQyu osQ xq.kuiQy dk lekdyu
% $
& &

∫ f′ ()xdx - rks d f () =′( )
f x
x
;fn dx
d d
af
x
x
{. ( )} - a f ()
dx dx
- & ′
x
.( ) =
x
∫ af′ () dx - af x a ∫ f′ ( ) dx
∫ af′ () dx - a ∫ f′ () dx
x
x
vFkkZr~ fdlh vpj vkSj iQyu osQ xq.kuiQy dk lekdy ml vpj vkSj iQyu osQ lekdy osQ xq.kuiQy osQ
cjkcj gksrk gSA

gy lfgr mnkgj.k

mnkgj.k 1- iQyu 15 dk osQ lkis{k lekdyu dhft,A
∫
∫ 15x dx - 15 x dx
4
4
gy %
15
5

c
- x + - ! / % mÙkj
5
∫ 7 dx
mnkgj.k 2- x dk eku Kkr dhft,A
∫ 7 dx - 7 dx = 7log| | c
x
+
gy% x ∫ x mÙkj
∫
mnkgj.k 3- 6sin x dx dk eku Kkr dhft,A