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find-f-x-0-pi-sin-2-t-1-2xcost-x-2-dt-with-x-lt-1-




Question Number 32482 by prof Abdo imad last updated on 25/Mar/18
find  f(x)= ∫_0 ^π      ((sin^2 t)/(1−2xcost +x^2 ))dt with ∣x∣<1 .
$${find}\:\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{\pi} \:\:\:\:\:\frac{{sin}^{\mathrm{2}} {t}}{\mathrm{1}−\mathrm{2}{xcost}\:+{x}^{\mathrm{2}} }{dt}\:{with}\:\mid{x}\mid<\mathrm{1}\:. \\ $$

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