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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

fJekJh^12 L nB[ebB L nB[ebB d/ nXkoG{s fB:w

sK n;hA efjzd/ jK fe dk fJZe nB[ebB (integral), f (x) j?. B'N

gqsheK dh ;jkfJsk Bkb fJ;B{z j/m nB[;ko fbyd/ jBL

fuzBQ “ ” nB[ebB dk gqshe j? fi;B{z nB[ebB fuzBQ (sign of integration) efjzd/ jB. fJj
cbB d/ nB[ebB B{z do;kT[Adk j?. dx ftZu x d[nkok fJj gqrN j[zdk j? fe nB[ebB (integration)
uo (variable) x d/ ;kg/y ehsk frnk j?. i/eo nB[ebB fe;h j'o uo d/ ;kg/y eoBk j't/, sK x
d/ ;EkB s/ uo B{z oZy fdzd/ jK.
;ze/s nzrq/Ih nZyo S dk fteqs o{g j?. n;b o{g ftZu nB[ebB :'r dh fJZe ftP/P ftXh j?

ns/ nzrq/Ih Ppd sum d/ gfjb/ nZyo S d[nkok jh ;ze/s pfDnk j?.

B'N; fe;h cbB dk nB[ebB (integration) eoB dh ftXh B{z nB[ebB eoBk (integration)
efjzd/ jB. fi; cbB dk nB[ebB ehsk iKdk j? T[;B{z nB[ebB (integrand) efjzd/
jB ns/ nB[ebB d[nkok gqkgs cbB B{z nB[ebB (integral) efjzd/ jB.

ftZu nB[ebB ns/ nB[ebB j?.

T[go'es toDB s'A ;gPN j? fe

ns/

x
fJ; soQK T[go'es cbBK ftZu cos x, sin x, e ns/ nB[ebB (integrand) jB ns/ sin x, –cos
x
x, e ns/ log t nB[ebB (integrals) jB.
fe;h cbB T[Zs/ eqw nB[;ko nB[ebB ns/ fBy/VB d'B'A fefonktK ehshnK ikD sK cbB nkgDh
n;b jkbs ftZu ofjzdk j?.

T[dkjoD ti',

Gkt, H

fJ; s'A ;gPN j[zdk j? fe fBy/VB ns/ nB[bB gqfsb'w fefonktK jB.

LOVELY PROFESSIONAL UNIVERSITY 183