Question Number 196950 by Erico last updated on 05/Sep/23 $$\mathrm{Prove}\:\mathrm{that}\:\underset{\:\mathrm{0}} {\int}^{\:\frac{\pi}{\mathrm{2}}} \frac{\mathrm{ln}\left(\mathrm{1}+\alpha\mathrm{sin}{t}\right)}{\mathrm{sin}{t}}{dt}=\:\frac{\pi^{\mathrm{2}} }{\mathrm{8}}−\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{arccos}\alpha\right)^{\mathrm{2}} \\ $$ Answered by Mathspace last updated on 06/Sep/23 $${f}\left({x}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{ln}\left(\mathrm{1}+{xsint}\right)}{{sint}}{dt}…
Question Number 196946 by Khalmohmmad last updated on 04/Sep/23 Answered by trisetyo last updated on 04/Sep/23 $$\mathrm{3}^{{x}} +\mathrm{2}^{{x}} =\mathrm{5} \\ $$$$\mathrm{3}^{{x}} =−\left(\mathrm{2}^{{x}} −\mathrm{5}\right)\vee\mathrm{2}^{{x}} =−\left(\mathrm{3}^{{x}} −\mathrm{5}\right)…
Question Number 196916 by peter frank last updated on 03/Sep/23 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 196917 by peter frank last updated on 03/Sep/23 Answered by MM42 last updated on 03/Sep/23 $$\:\:\frac{\mid{PA}\mid}{\mid{PB}\mid}\:=\:\mathrm{3}\:\:\checkmark \\ $$ Commented by peter frank last…
Question Number 196934 by Amidip last updated on 03/Sep/23 Answered by aleks041103 last updated on 04/Sep/23 $${M}\left({x},{y}\right){dx}+{N}\left({x},{y}\right){dy}=\mathrm{0} \\ $$$${if}\:\:\partial_{{y}} {M}=\partial_{{x}} {N},\:{then}\:\exists{F}\left({x},{y}\right): \\ $$$${M}\left({x},{y}\right){dx}+{N}\left({x},{y}\right){dy}={dF}=\mathrm{0}\Rightarrow{F}={const}. \\ $$$${in}\:{our}\:{case}\:\partial_{{y}}…
Question Number 196918 by cortano12 last updated on 03/Sep/23 Answered by MM42 last updated on 03/Sep/23 $${a}_{{n}} =\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{5}×\mathrm{3}^{{n}−\mathrm{1}} −\mathrm{1}\right)\:\checkmark \\ $$ Terms of Service Privacy…
Question Number 196935 by keiner last updated on 03/Sep/23 $$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 196928 by SANOGO last updated on 03/Sep/23 $${I}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {sin}^{{n}} {x}\:{dx} \\ $$ Commented by Frix last updated on 03/Sep/23 $$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}}…
Question Number 196929 by Amidip last updated on 03/Sep/23 Answered by som(math1967) last updated on 03/Sep/23 $$\mathrm{2}{U}_{\mathrm{6}} −\mathrm{3}{U}_{\mathrm{4}} +\mathrm{1} \\ $$$$=\mathrm{2}\left({sin}^{\mathrm{6}} \alpha+{cos}^{\mathrm{6}} \alpha\right)−\mathrm{3}\left({sin}^{\mathrm{4}} \alpha+{cos}^{\mathrm{4}} \right)+\mathrm{1}…
Question Number 196914 by SANOGO last updated on 03/Sep/23 Answered by witcher3 last updated on 03/Sep/23 $$−\frac{\mathrm{1}}{\mathrm{n}+\mathrm{1}}>−\frac{\mathrm{1}}{\mathrm{n}} \\ $$$$\mathrm{I}_{\mathrm{n}} =\left[−\frac{\mathrm{1}}{\mathrm{n}},\mathrm{1}\right] \\ $$$$\mathrm{I}_{\mathrm{n}+\mathrm{1}} \:\:\subseteq\mathrm{I}_{\mathrm{n}} \:\:\mathrm{suite}\:\mathrm{decroissante}\:\mathrm{minore} \\…