Question Number 115362 by Bird last updated on 25/Sep/20 $${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{sinx}}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$ Answered by TANMAY PANACEA last updated on 25/Sep/20 $$\mathrm{1}\geqslant{sinx}\geqslant−\mathrm{1} \\…
Question Number 115361 by Bird last updated on 25/Sep/20 $${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left(\pi{x}^{\mathrm{2}} \right)}{\left({x}^{\mathrm{2}} +\mathrm{3}\right)^{\mathrm{2}} }{dx} \\ $$ Answered by Olaf last updated on 27/Sep/20 $$\frac{\pi\left[\mathrm{6}\pi\left(\boldsymbol{\mathrm{C}}\left(\sqrt{\mathrm{6}}\right)−\boldsymbol{\mathrm{S}}\left(\sqrt{\mathrm{6}}\right)\right)+\boldsymbol{\mathrm{C}}\left(\sqrt{\mathrm{6}}\right)−\boldsymbol{\mathrm{S}}\left(\sqrt{\mathrm{6}}\right)+\sqrt{\mathrm{6}}−\mathrm{1}\right]}{\mathrm{12}\sqrt{\mathrm{3}}}…
Question Number 49816 by Aditya789 last updated on 11/Dec/18 $$\frac{\mathrm{sin}^{\mathrm{6}} \mathrm{x}−\mathrm{cos}^{\mathrm{6}} \mathrm{x}}{\mathrm{sin}^{\mathrm{2}} \mathrm{xcos}^{\mathrm{2}} \mathrm{x}}.\mathrm{intregrate} \\ $$ Answered by AdqhK ÐQeQqQ last updated on 11/Dec/18 $$\int\frac{\left({sin}^{\mathrm{2}}…
Question Number 49815 by Aditya789 last updated on 11/Dec/18 $$\mathrm{sin}^{\mathrm{6}} \mathrm{x}−\mathrm{cos}^{\mathrm{6}} \mathrm{x}/\mathrm{sin}^{\mathrm{2}} \mathrm{xcos}^{\mathrm{2}} \mathrm{x} \\ $$ Commented by Abdo msup. last updated on 12/Dec/18 $${if}\:{you}\:{mean}\:{simification}…
Question Number 49806 by maxmathsup by imad last updated on 10/Dec/18 $${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {ln}\left(\mathrm{1}−{x}^{\mathrm{2}} {cos}\theta\right){d}\theta\:\:\:{with}\:\:\mid{x}\mid<\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {ln}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{4}}{cos}\theta\right){d}\theta\:. \\ $$ Commented by…
Question Number 49761 by rahul 19 last updated on 10/Dec/18 $${Calculate}\:: \\ $$$$\:\int\frac{\:\:\mathrm{sin}^{\mathrm{2}} {x}\:\mathrm{cos}^{\mathrm{2}} {x}}{\left(\mathrm{sin}^{\mathrm{3}} {x}+\mathrm{cos}^{\mathrm{3}} {x}\right)^{\mathrm{2}} }\:{dx} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated…
Question Number 49760 by rahul 19 last updated on 10/Dec/18 Commented by rahul 19 last updated on 11/Dec/18 $${Thank}\:{you}\:{sir}! \\ $$ Commented by tanmay.chaudhury50@gmail.com last…
Question Number 49746 by rahul 19 last updated on 10/Dec/18 $$\int\frac{\mathrm{sin}^{\mathrm{8}} {x}−\mathrm{cos}^{\mathrm{8}} {x}}{\mathrm{1}−\mathrm{2sin}^{\mathrm{2}} {x}.\mathrm{cos}^{\mathrm{2}} {x}}\:=\:? \\ $$$$\left.{a}\left.\right)\left.\:\frac{−\mathrm{1}}{\mathrm{2}}\mathrm{sin}\:\mathrm{2}{x}\:\:\:{b}\right)\frac{\mathrm{1}}{\mathrm{2}}\mathrm{sin}\:\mathrm{2}{x}\:\:\:{c}\right){None}. \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on…
Question Number 115267 by bobhans last updated on 24/Sep/20 $${If}\:{f}\left({x}\right)\:{is}\:{a}\:{differentiable}\:{function} \\ $$$${defined}\:\:\forall{x}\in\mathbb{R}\:{such}\:{that}\:\left({f}\left({x}\right)\right)^{\mathrm{3}} −{x}+{f}\left({x}\right)=\mathrm{0} \\ $$$${then}\:\underset{\mathrm{0}} {\overset{\sqrt{\mathrm{2}}} {\int}}\:{f}^{−\mathrm{1}} \left({x}\right)\:{dx}\:=\: \\ $$ Answered by Olaf last updated…
Question Number 180786 by Vynho last updated on 17/Nov/22 $${f}\left({t}\right)=\int_{\mathrm{0}} ^{{t}} {x}−\lfloor{x}\rfloor\:\:{dx} \\ $$ Answered by mr W last updated on 17/Nov/22 $${let}\:{n}=\lfloor{t}\rfloor \\ $$$${f}\left({t}\right)=\underset{{k}=\mathrm{0}}…