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

fJekJh^15 L fBPfus nB[ebB

B'N

15H3 fBPfus nB[ebBK ftZu gqfs;EkgB
(Substitution in Definite Integration)
nfBPfus nBe[bB dh soQK edh^edh nB[ebB ftZu th uo B{z pdbBk io{oh j' iKdk j?.
fefonk^ftXh ;ob pDh oj/ fJ; soQK gqfs;EkgB d/ Bkb^Bkb ;hwktK B{z th pdb fdZsk iKdk j?.
T[dkjoD ti', wzB fbU fe n;hA ψ(x) = t oZyhJ/ sK

eh s[;hA ikDd/ j' i/eo uo x d/ bJh nB[ebB ;hwktK a ns/ b sZe j'D, sK t d/ bJh ;hwktK
;zpzX t = ψ(x) s'A ehsh iKdh j?.

∴id'A x = a, T[d'A t = ψ (a) ns/ id'A x = b, T[d'A t = ψ (b)H
∴

jZb ;fjs T[dkjoD
T[dkjoD 1H dk wkB gsk eo'.

jZb L wzB fbU log x = t sK (1/x) dx = dt

id'A

ns/ id'A

∴

T[Zso

T[dkjoD 2H dk wkB gsk eo'.

2
jZb L wzB fbU x = tan θ; ∴ dx = sec θ dθ
id'A x = 0, sK tan θ = 0 Gkt θ = 0

ns/ id'A x = 1, sK tan θ = 1 Gkt θ =

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