Question Number 172872 by mnjuly1970 last updated on 02/Jul/22 $$ \\ $$$$\:\:\:\:\:\mathrm{lim}_{\:{x}\rightarrow\:\mathrm{0}^{+} } \left({x}^{\:\frac{\mathrm{1}}{\mathrm{l}{n}\left({xsin}\left({x}^{\mathrm{3}} \right)\right)}} \right)=? \\ $$$$ \\ $$$$ \\ $$ Answered by mnjuly1970…
Question Number 107314 by bemath last updated on 10/Aug/20 $$\:\:\:\:\:\:\:\:\doublebarwedge{bemath}\doublebarwedge \\ $$$$\:\:\:\:\:\underset{\mathrm{0}} {\overset{\mathrm{2}\pi} {\int}}\:\mathrm{ln}\:\left(\mathrm{1}+\mathrm{sin}\:{x}\right)\:{dx}\:? \\ $$ Answered by mnjuly1970 last updated on 10/Aug/20 $$\Omega=\int_{\mathrm{0}} ^{\:\mathrm{2}\pi}…
Question Number 172847 by Mikenice last updated on 02/Jul/22 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 41762 by math khazana by abdo last updated on 12/Aug/18 $${let}\:{f}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{ln}\left(\mathrm{1}+{xt}^{\mathrm{2}} \right)}{\mathrm{1}+{t}^{\mathrm{2}} }\:{dt} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{simple}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{ln}\left(\mathrm{1}+{t}^{\mathrm{2}} \right)}{\mathrm{1}+{t}^{\mathrm{2}} }{dt}…
Question Number 107291 by mathmax by abdo last updated on 09/Aug/20 $$\mathrm{let}\:\mathrm{x}\in\mathrm{R}−\left\{\mathrm{1},−\mathrm{1}\right\}\:\mathrm{explicit}\:\mathrm{the}\:\mathrm{function} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\mathrm{ln}\left(\mathrm{x}^{\mathrm{2}} −\mathrm{2xcos}\theta\:+\mathrm{1}\right)\mathrm{d}\theta \\ $$$$ \\ $$ Answered by Ar Brandon…
Question Number 107286 by mathmax by abdo last updated on 09/Aug/20 $$\mathrm{let}\:\mathrm{f}_{\mathrm{n}} \left(\mathrm{x}\right)\:=\mathrm{ne}^{−\mathrm{nx}} \:\:\mathrm{calculate}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{f}_{\mathrm{n}} \left(\mathrm{x}\right)\mathrm{dx} \\ $$$$\mathrm{and}\:\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \mathrm{f}_{\mathrm{n}} \left(\mathrm{x}\right)\mathrm{dx}\:\:\mathrm{is}\:\mathrm{the}\:\mathrm{convergence}\:\mathrm{uniform}\:\mathrm{on}\:\left[\mathrm{0},\mathrm{1}\right]? \\…
Question Number 172823 by Mikenice last updated on 01/Jul/22 Answered by thfchristopher last updated on 03/Jul/22 $$\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{cot}^{−\mathrm{1}} \left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right){dx} \\ $$$$=\left[{x}\mathrm{cot}^{−\mathrm{1}} \left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)\right]_{\mathrm{0}}…
Question Number 172822 by Mikenice last updated on 01/Jul/22 Answered by Mathspace last updated on 02/Jul/22 $${question}\:{not}\:{clear}\:{do}\:{you}\: \\ $$$${mean}\:\sqrt{{x}}{or}\:\Gamma\left({x}\right)… \\ $$ Terms of Service Privacy…
Question Number 107285 by mathmax by abdo last updated on 09/Aug/20 $$\mathrm{find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{arctan}\left(\mathrm{2x}\right)}{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\mathrm{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 107283 by mathmax by abdo last updated on 09/Aug/20 $$\mathrm{f}\:\mathrm{integrable}\:\mathrm{continue}\:\mathrm{on}\:\left[\mathrm{a},\mathrm{b}\right]\:\mathrm{let}\:\mathrm{m}\:=\mathrm{inf}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{and}\:\mathrm{M}=\mathrm{sup}\:\mathrm{f}\left(\mathrm{x}\right) \\ $$$$\left(\mathrm{x}\:\in\left[\mathrm{a},\mathrm{b}\right]\:\mathrm{prove}\:\mathrm{that}\:\:\:\:\:\:\:\left(\mathrm{b}−\mathrm{a}\right)^{\mathrm{2}} \leqslant\int_{\mathrm{a}} ^{\mathrm{b}} \mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}×\int_{\mathrm{a}} ^{\mathrm{b}} \:\frac{\mathrm{dx}}{\mathrm{f}\left(\mathrm{x}\right)}\leqslant\frac{\left(\mathrm{b}−\mathrm{a}\right)^{\mathrm{2}} }{\mathrm{4}}\frac{\left(\mathrm{m}+\mathrm{M}\right)^{\mathrm{2}} }{\mathrm{mM}}\right. \\ $$ Terms of…