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VED1
E L-LOVELY-H math12-1 IInd 6-8-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 VIth 10-9-12

noEPk;soh dk rfDs Hitesh Jhanji, Lovely Professional University

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

(Integration : Basic Rules of Integration)

ftP/ t;s{ (Contents)
T[d/P (Objectives)
gq;sktBk (Introduction)

12H1 ftnkge nB[ebB (Comprehensive Integrals)
12H2 wkBe nB[ebB (Standard Integral)

n
12H3 x dk x d/ ;kg/y nB[ebB, fiZE/ n ≠–1.
n
(Integration of x Relative to x, Where n ≠–1)
12H4 fe;h nuo ns/ fJZe cbB d/ r[DBcb dk nB[ebB
(Integration of the Multiplication of a Constant and a Function)
12H5 cbBK d/ :'rcb iK nzso dk nB[ebB
(Integration of the Sum and Subtract of the Functions)
12H6 ;koKP (Summary)

12H7 Ppde'P (Keywords)
12H8 nfGnk; gqPB (Review Questions)
12H9 ;zdoG g[;seK (Further Readings)

T[d/P (Objectives)

fJ; fJekJh d/ nfXn?B s'A pknd ftfdnkoEh :'r j'Dr/L
• ftnkge nB[ebB B{z jZb eoB ftZu.

• wkBe nB[ebB B{z ;wMD ;zpzXh.
n
• x dk x d/ ;kg/y nB[ebB, fiZE/ n≠1, Bkb ;zpzXs ;wZf;nktK B{z jZ beoB ;zpzXh.
• fe;h nuo ns/ fJZe cbB d/ r[DBcb dk nB[ebB eZYD ;zpzXh.
• cbBK d[nkok :'rcb iK nzso dk nB[ebB eoB ;zpzXh.

gq;sktBk (Introduction)

cbB dk nB[ebB (Integration of the Function)^fe;h cbB dk fBy/VB gsk eoB dh gqfsb'w
(Inverse) fefonk B{z nB[ebB (Integration) efjzd/ jB. fBy/VB rfDs ftZu n;hA fdZs/ j'J/
cbB dk fBy/VB r[DKe (differential coefficient) gsk eod/ jK, gozs{ nB[ebB^rfDs ftZu ;kB{z
T[jBK cbBK B{z gsk eoBk j[zdk j? fiBQK dk fBy/VB r[DKe fdZsk j'fJnkj?.
T[dkjoE ti'A, sin x dk x dk ;kg/y fBy/VB eoB s/ nfBy/VB r[DKe cos x j[zdk j? sK cbB cos
x dk x d/ ;kg/y nB[ebB eoB s/ nB[ebB (integral) sin x j't/rk.
wzB fbU f (x), x dk e'Jh cbB j? fi;dk fBy/VB r[DKe f ′ (x) j?, Gkt
d
{ ()} = f ′ () x
fx
dx

182 LOVELY PROFESSIONAL UNIVERSITY