find-F-x-0-pi-ln-1-x-sin-2-t-dt-with-x-lt-1-2-calculate-0-pi-ln-1-1-2-sin-2-t-dt-

Tinku Tara June 4, 2023 Integration 0 Comments

Question Number 35046 by math khazana by abdo last updated on 14/May/18

find F(x)= ∫_0 ^π ln( 1+x sin^2 t)dt with ∣x∣<1 2) calculate ∫_0 ^π ln(1+(1/2)sin^2 t)dt

$${find}\:{F}\left({x}\right)=\:\int_{\mathrm{0}} ^{\pi} \:{ln}\left(\:\mathrm{1}+{x}\:{sin}^{\mathrm{2}} {t}\right){dt}\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\pi} \:\:{ln}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}{sin}^{\mathrm{2}} {t}\right){dt} \\ $$

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find-F-x-0-pi-ln-1-x-sin-2-t-dt-with-x-lt-1-2-calculate-0-pi-ln-1-1-2-sin-2-t-dt-

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