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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
B'N T[dkjkoD 2H f;ZX eo' fe
À/2 À/2
x sin x dx = 2 x sin x dx
∫ -À/2 ∫ 0
À/2
ns/ x cos x dx = 0.
∫ -À/2
jZb L fJZE/ cbB f (x) = x sin x
∴ f (–x) = (–x) sin (–x) = x sin x = f (x)
fJ; soQK cbB fi;s j?
∴ −π ∫ π /2 /2 x sin x dx = 2 0 ∫ π /2 x sin x dx
i/eo f (x) = x cos x
∴ f (–x) = (–x) cos (–x) = – x cos x = – f (x)
fJ; bJh cbB NKe j?.
∴ −π ∫ π /2 /2 x cos x dx = 0.
T[dkjoD 3L f;ZX eo' fe
À/2
x
sin 2 log tan x dx = 0.
∫ 0
jZb L wzfBnk ....(i)
....(ii)
;wheoD (i) ns/ (ii) B{z i'V s/,
∴ I = 0
242 LOVELY PROFESSIONAL UNIVERSITY
