Question Number 210126 by mnjuly1970 last updated on 31/Jul/24 Answered by Frix last updated on 31/Jul/24 $$\mathrm{These}\:\mathrm{substitutions}\:\mathrm{make}\:\mathrm{it}\:\mathrm{easy}\:\mathrm{to}\:\mathrm{see} \\ $$$$\mathrm{what}'\mathrm{s}\:\mathrm{going}\:\mathrm{on}: \\ $$$$ \\ $$$$\mathrm{Let}\:{x}=\mathrm{sin}\:\alpha\:\overset{\left[\mathrm{differentiate}\right]} {\Rightarrow} \\…
Question Number 210127 by essaad last updated on 31/Jul/24 Answered by lepuissantcedricjunior last updated on 01/Aug/24 $$\int_{\mathrm{1}} ^{\mathrm{2}} \frac{\boldsymbol{{ln}}\left(\mathrm{1}+\boldsymbol{{x}}\right)−\boldsymbol{{lnx}}}{\boldsymbol{{x}}^{\mathrm{2}} }\boldsymbol{{dx}}=\int_{\mathrm{1}} ^{\mathrm{2}} \frac{\boldsymbol{{ln}}\left(\mathrm{1}+\boldsymbol{{x}}\right)}{\boldsymbol{{x}}^{\mathrm{2}} }\boldsymbol{{dx}}−\int_{\mathrm{0}} ^{\mathrm{2}} \frac{\boldsymbol{{lnx}}}{\boldsymbol{{x}}^{\mathrm{2}}…
Question Number 210120 by emilagazade last updated on 31/Jul/24 Answered by mr W last updated on 31/Jul/24 Commented by mr W last updated on 31/Jul/24…
Question Number 210122 by SonGoku last updated on 31/Jul/24 Commented by SonGoku last updated on 31/Jul/24 $$\mathrm{How}\:\mathrm{do}\:\mathrm{I}\:\mathrm{find}\:\mathrm{the}\:\mathrm{painted}\:\mathrm{area}? \\ $$ Answered by mr W last updated…
Question Number 210133 by SANOGO last updated on 31/Jul/24 $${calcul} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \left[{nt}^{{n}−\mathrm{1}} \left(\mathrm{1}−{t}\right)−{t}^{{n}} \right]{dt} \\ $$ Answered by mr W last updated on…
Question Number 210098 by klipto last updated on 30/Jul/24 $$\boldsymbol{\mathrm{show}}\:\boldsymbol{\mathrm{that}} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{\mathrm{lnx}}}{\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{1}}\boldsymbol{\mathrm{dx}}=\frac{\boldsymbol{\pi}^{\mathrm{2}} }{\mathrm{8}} \\ $$ Commented by AlagaIbile last updated on 30/Jul/24…
Question Number 210095 by AlagaIbile last updated on 30/Jul/24 Commented by TonyCWX08 last updated on 01/Aug/24 $${Are}\:{you}\:{El}\:{Matematico}? \\ $$ Answered by Spillover last updated on…
Question Number 210090 by Tawa11 last updated on 30/Jul/24 Commented by mr W last updated on 30/Jul/24 $${are}\:{there}\:\mathrm{3}\:{times}\:{letter}\:{p}\:{in}\:{your}\: \\ $$$${picture}? \\ $$ Commented by Tawa11…
Question Number 210091 by mr W last updated on 30/Jul/24 $${find}\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{2}{n}^{\mathrm{2}} }\right)=? \\ $$ Commented by AlagaIbile last updated on 30/Jul/24 $$\:\:\underset{{n}=\mathrm{1}}…
Question Number 210085 by Ismoiljon_008 last updated on 30/Jul/24 $$ \\ $$$$\:\:\frac{\mathrm{1}}{\frac{\mathrm{1}}{\mathrm{2003}}+\frac{\mathrm{1}}{\mathrm{2004}}+\frac{\mathrm{1}}{\mathrm{2005}}+\frac{\mathrm{1}}{\mathrm{2006}}+\frac{\mathrm{1}}{\mathrm{2007}}+\frac{\mathrm{1}}{\mathrm{2008}}+\frac{\mathrm{1}}{\mathrm{2009}}}\:=\:? \\ $$$$\:\:\:\mathscr{H}{elp}\:{me} \\ $$$$ \\ $$ Answered by Frix last updated on 30/Jul/24…