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E L-LOVELY-H math13-1 IInd 21-10-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12
fJekJh^13 L nB[ebB dhnK ftXhnK
13H4 nB[ebe (Integrand) B'N
i/eo nB[ebe (Integrand) φ [f (x)] (x) d/ o{g dk j't/ Gkt fJj fe;h okPh f (x) d/ cbB ns/
fJ;h okPh f (x) d/ fBy/VB r[DKe dk r[DBcb j't/ iK fJ; o{g ftZu fbfynk ik ;edk j't/
sK n;hA fJ; okPh f (x) B{z t d/ pokpo wkB e/ nB[ebB eod/ jB.
B'N; i/eo f (x) = t sK (x) dx = dt
∴ (wzB fbU)
= ψ [φ(x)], [t dk wkB oZyD s/]
jZb ;fjs T[dkjoD
T[dkjoD 1H dk wkB gsk eo'.
jZb L wzB fbU sin x = t cos x dx = dt.
fJ; soQK
T[Zso
T[dkjoD 2H dk wkB gsk eo'.
jZb L wzB fbU wzB fbU sK
∴
& T[Zso
T[dkjoD 3H dk wkB gsk eo'.
jZb L wzB fbU
∴ T[Zso
T[dkjoD 4H dk wkB gsk eo'.
jZb L wzB fbU log x = t dx = dt
LOVELY PROFESSIONAL UNIVERSITY 205
