Page 218 - DECO403_MATHEMATICS_FOR_ECONOMISTS_PUNJABI

VED1
E L-LOVELY-H math14-1 IInd 6-8-11 IIIrd 24-1-12 IVth 21-4-12 Vth 10-9-12

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

B'N fJekJh^14L :'r (i'V) d/ o{g ftZu nB[ebB

(Integration as a Summation)

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

14H1 d' cbBK d/ r[DB dk nB[ebB (tzfvnk j'fJnk nB[ebB) gsk eoBk [Finding
Integral of Multiplication of Two Functions (Divided Integration)]
14H2 nzfPe fGzBK d[nkok nB[ebB (Integration by Partial Fractions)

14H3 d' wkBe nB[ebB (Two Standard Integral)
14H4 ;koKP (Summary)
14H5 Ppde'P (Keywords)

14H6 nfGnk; gqPB (Review Questions)
14H7 ;zdoG g[;seK (Further Readings)

T[d/P (Objectives)

fJ; fJekJh d/ nfXn?B s'A pknd ftfdnkoEh :'r j'Dr/L
• d' cbBK d/ r[DB dk nB[ebB gsk eoB ;zpzXh.

• nzfPe fGzBK d[nkok nB[ebB gsk eoB ftZu.
• d' wkBe nB[ebB dh ikDekoh gqkgs eoB ftZu.

gq;sktBk (Introduction)

nB[ebB fB:w dk gq:'r eoB s'A gfjbK ;kB{z fJj d/yDk ukjhdk j? fe fefonk B{z fJZe iK d'
tko eoB s/ nB[ebe iK sK fe;h gqwkfDe nB[ebe dk o{g b? bJ/ iK nfij/ o{g ftZu nk ikJ/
fi;dk nB[ebB ehsk ik ;e/. i/eo d' cbBK ftZu'A fJZe cbB nfijk j't/ fi;dk nB[ebB ;kB{z
gsk Bk j't/, sK T[; cbB B{z ;dk gfjbk cbB wzBDk ukjhdk j?. i/eo ;Zi/ gZy ftZu nB[ebB
foD fuzBQ d/ Bkb nkgD/ gfjb/ o{g ftZu nk iKdk j? sK ;wheoD jZb eoB ftZU fB:wK dk gq:'r
eoe/ gqPB jZb eoBk ukjhdk j?.

14H1 d' cbBK d/ r[DB dk nB[ebB (tzfvnk j'fJnk nB[ebB) gsk eoBk
[Finding Integral of Multiplication of Two Functions (Divided
Integral]

i/eo f (x) ns/ cbB φ(x) dk r[DB f (x). φ(x) j't/ sK T[;dk fBy/VB
d
φ
x φ
x ′ φ
f
x
x x
{ (). ()} = f () () + f ′ () ()
x
dx
d'jK gZyK dk x d/ ;kg/y nB[ebB eoB s/

212 LOVELY PROFESSIONAL UNIVERSITY