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VED1
E L-LOVELY-H math15-1 IInd 6-8-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 Vth 10-9-12

noEPk;soh dk rfDs Pavitar Parkash Singh, Lovely Professional University

B'N fJekJh^15L fBPfus nB[ebB

(Definite Integration)

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

15H1 nB[ebB dhnK ;hwktK (Limitations of Integration)
15H2 fBPfus nB[ebB gsk eoB dh ftXh (Method of Finding Definite Integration)

15H3 fBPfus nB[ebBK ftZu gqfs;EkgB (Substitution in Definite Integration)
15H4 fBPfus nB[ebB d/ ;XkoD r[D (General Properties of Definite Integrals)
15H5 nBzs ;hwk tkb/ nB[ebB (Integral of Infinity Limits)

15H6 ;koKP (Summary)
15H7 Ppde'P (Keywords)

15H8 nfGnk; gqPB (Review Questions)
15H9 ;zdoG g[;seK (Further Readings)

T[d/P (Objectives)

fJ; fJekJh d/ nfXn?B s'A pknd ftfdnkoEh :'r j'Dr/L
• fBPfus nB[ebB d/ noE, ;hwktK ns/ gsk eoB dh ftXh B{z ikDBr/.

• fBPfus nB[ebBK ftZu gqfs;EkgB B{z ;wM ;eDr/.
• fBPfus nB[ebB d/ ;XkoD r[D B{z ikD ;eDr/.

• nBzs ;hwk tkb/ nB[ebB dh ikDekoh fwb/rh.

gq;sktBk (Introduction)

wzB fbU x d/ ;kg/y cbB f (x) dk nB[ebB (integral), F (x) j?.
i/eo ;[szso uo x d/ d' fBod/fPs wkBK (values), wzB fbU, a ns/ b d/ bJh cbB f (x) d/
nB[ebB F (x) d/ wkBK ftZu nzso F (b) – F (a) j?, sK fJ; nzso B{z nzsokb [a, b] d/ bJh
f(x) dk fBPfus nB[ebB (Definite Integral) efjzd/ jB ns/ fJ;B{z nZr/ fby/ nB[;ko gqrN
eoKr/^
a ∫ b f () dx
x
fBPfus nB[ebB dk noE^id'A fe;h cbB dk nB[ebB, fe;/ d' fBPfus ;hwktK d/ bJh
gsk ehsk iKdk j? sK T[;B{z fBPfus nB[ebB (definite integral) efjzd/ jB.

∫
x
x
i/eo f () dx = F ()
sK a ∫ b f () dx = [ ()] = F ( ) F ( )
−
b
b
a
x
F
x
a

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