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Author: Tinku Tara

Question-127519

Question Number 127519 by O Predador last updated on 30/Dec/20 Answered by mahdipoor last updated on 30/Dec/20 $$\mathrm{0}.\mathrm{0833}…=\mathrm{0}.\mathrm{08}\overset{−} {\mathrm{3}}=\mathrm{0}.\mathrm{08}+\mathrm{0}.\mathrm{00}\overset{−} {\mathrm{3}}= \\ $$$$\frac{\mathrm{8}}{\mathrm{100}}+\frac{\mathrm{1}}{\mathrm{300}}=\frac{\mathrm{25}}{\mathrm{300}}=\frac{\mathrm{1}}{\mathrm{12}}=\frac{\mathrm{1}×\mathrm{2}}{\mathrm{1}×\mathrm{2}×\mathrm{3}×\mathrm{4}}=\frac{\mathrm{2}!}{\mathrm{4}!}=\frac{\left[{log}_{\mathrm{2}} \left({x}^{\mathrm{2}} \right)−\mathrm{2}\right]!}{\left[{log}_{\mathrm{2}} \left({x}\right)+\mathrm{2}\right]!}…

let-f-x-0-1-ln-1-xt-3-dt-with-x-lt-1-1-find-a-explicit-form-of-f-x-2-calculate-0-1-ln-1-1-2-t-3-dt-3-calculate-A-0-1-ln-1-sin-t-3-dt-with-0-lt-lt-pi-2-

Question Number 61978 by maxmathsup by imad last updated on 13/Jun/19 $${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}−{xt}^{\mathrm{3}} \right){dt}\:\:{with}\:\:\mid{x}\mid<\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}−\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}{t}^{\mathrm{3}} \right){dt} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:{A}\left(\theta\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}}…