Page 229 - 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¡

Lo&ewY;kadu
uksV

fjDr LFkkuksa dh iwfrZ djsa @@
+ @
E
µ

1- izfrLFkkiu lafØ;k esa fn, x, lekdY; dks ekud lw=kksa esa ifjofrZr djosQ --------- fd;k tkrk gSA
2- ∫ sin (ax + ) b dx = − 1 cos (.........) + c
a

3- ∫ sec ax + dx = ......... + c
2
a

4- ;fn osQ iQyu esa --------- dk xq.kuiQy fn;k jgrk gS rks ml iQyu dk lekdyu - # ekudj
fd;k tk ldrk gSA

13-4 lekdY;
%

;fn lekdY;
,
φ 0 1 ′ osQ :i dk gks vFkkZr~ ;g fdlh jkf'k osQ iQyu rFkk blh
jkf'k osQ vody xq.kkad ′ dk xq.kuiQy gks ;k bl :i esa fy[kk tk ldrk gks rks ge bl jkf'k

dks # osQ cjkcj ekudj lekdyu djrs gSaA

uksV~l ;fn - # rks ′ ! - !#

t
x
∴ ∫ φ [( )] f′ f x ( ) dx - ∫ φ ()tdt = ψ ( ) (eku yks)
- ψ 0φ 1. 0# dk eku j[kus ij1

gy lfgr mnkgj.k

∫
4
mnkgj.k 1- sin x cos xdx dk eku Kkr dhft,A
gy % eku yks

- # ⇒
! - !#
4
∫ sin x .cosxdx - ∫ tdt
4
vr%
t 5 1
- / % -

/ % mÙkj

5 5
∫
θ
mnkgj.k 2- cot 3 . θ 2 θ cosec d dk eku Kkr dhft,A
gy % eku yks cot θ ∫ 3 . cosec θ 2 d θ eku yks θ - rks 2
θ !θ - !

⇒
θ !θ - 2 !
3
∫
θ
∴ ∫ cot θ 3 cosec θ 2 d - 2 x dx - 2 x 4 4 / %
4
cot θ
-2 / % mÙkj
4