Question Number 201348 by sonukgindia last updated on 05/Dec/23 Answered by aleks041103 last updated on 05/Dec/23 $${I}=\int_{\mathrm{0}} ^{\:\pi/\mathrm{2}} {ln}\left({sin}\left({x}\right)\right){dx} \\ $$$${u}=\pi/\mathrm{2}−{x}\Rightarrow{du}=−{dx} \\ $$$$\Rightarrow{I}=\int_{\mathrm{0}} ^{\:\pi/\mathrm{2}} {ln}\left({cos}\left({u}\right)\right){du}…
Question Number 201349 by sonukgindia last updated on 05/Dec/23 Answered by Sutrisno last updated on 05/Dec/23 $${misal}\:: \\ $$$${A}\:=\:\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}{ln}\left({cosx}\right)\:{dx} \\ $$$${B}\:=\:\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}{ln}\left({sinx}\right)\:{dx}…
Question Number 201350 by sonukgindia last updated on 05/Dec/23 Answered by Calculusboy last updated on 05/Dec/23 $$\boldsymbol{{Solution}}:\:\boldsymbol{{let}}\:\boldsymbol{{y}}=\frac{\boldsymbol{\pi}}{\mathrm{4}}−\boldsymbol{{x}}\:\:\:\boldsymbol{{dy}}=−\boldsymbol{{dx}} \\ $$$$\boldsymbol{{when}}\:\boldsymbol{{x}}=\frac{\boldsymbol{\pi}}{\mathrm{4}}\:\:\boldsymbol{{y}}=\mathrm{0}\:\:\boldsymbol{{and}}\:\boldsymbol{{when}}\:\boldsymbol{{x}}=\mathrm{0}\:\boldsymbol{{y}}=\frac{\boldsymbol{\pi}}{\mathrm{4}} \\ $$$$\boldsymbol{{I}}=\int_{\frac{\boldsymbol{\pi}}{\mathrm{4}}} ^{\mathrm{0}} \boldsymbol{{In}}\left[\mathrm{1}+\boldsymbol{{tan}}\left(\frac{\boldsymbol{\pi}}{\mathrm{4}}−\boldsymbol{{y}}\right)\right]−\boldsymbol{{dy}}\:\:\:\:\left(\boldsymbol{{change}}\:\boldsymbol{{of}}\:\boldsymbol{{variable}}\right) \\ $$$$\boldsymbol{{I}}=\int_{\mathrm{0}}…
Question Number 201351 by sonukgindia last updated on 05/Dec/23 Answered by Sutrisno last updated on 05/Dec/23 $$=\int_{\mathrm{0}} ^{\pi} \frac{{x}}{\mathrm{1}+{sinx}}.\frac{\mathrm{1}−{sinx}}{\mathrm{1}−{sinx}}{dx} \\ $$$$=\int_{\mathrm{0}} ^{\pi} \frac{{x}−{xsinx}}{\mathrm{1}−{sin}^{\mathrm{2}} {x}}{dx} \\…
Question Number 201346 by sonukgindia last updated on 05/Dec/23 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 201411 by MrGHK last updated on 05/Dec/23 Commented by mr W last updated on 06/Dec/23 $${Mr}\:{Laplac}:\:{please}\:{post}\:{your}\:{answer} \\ $$$${in}\:{the}\:{thread}\:{corresponding}\:{to}\:{the} \\ $$$${question}!\:{otherwise}\:{it}'{s}\:{not}\:{clear} \\ $$$${what}\:{your}\:{post}\:{is}\:{for}. \\…
Question Number 201332 by Rodier97 last updated on 04/Dec/23 $$ \\ $$$$ \\ $$$$ \\ $$$$\:\:\:\:{calcul}\:: \\ $$$$ \\ $$$$\:\:\:\:\mathrm{1}.\:\:\:\:{lim}_{{n}\rightarrow+\infty\:} \frac{{sin}\left({n}^{\mathrm{2}} \right)−{cos}\left({n}^{\mathrm{3}} \right)}{{n}}\: \\ $$$$…
Question Number 201329 by MrGHK last updated on 04/Dec/23 Answered by witcher3 last updated on 04/Dec/23 $$=\underset{\mathrm{n}\geqslant\mathrm{0}} {\sum}\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} }{\mathrm{2n}+\mathrm{1}}\underset{\mathrm{m}\geqslant\mathrm{0}} {\sum}\left(−\mathrm{1}\right)^{\mathrm{m}} \int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{x}^{\mathrm{m}+\mathrm{2n}+\mathrm{1}} \mathrm{dx} \\…
Question Number 201325 by sonukgindia last updated on 04/Dec/23 Commented by mr W last updated on 05/Dec/23 $${do}\:{you}\:{have}\:{the}\:{right}\:{answer}? \\ $$ Answered by mr W last…
Question Number 201292 by sonukgindia last updated on 03/Dec/23 Answered by aleks041103 last updated on 03/Dec/23 $${I}=\underset{−{a}} {\overset{{a}} {\int}}\frac{{cos}\left({x}\right){dx}}{\mathrm{1}+{e}^{\pi/{x}} }=\underset{{a}} {\overset{−{a}} {\int}}\frac{{cos}\left(−{x}\right){d}\left(−{x}\right)}{\mathrm{1}+{e}^{\pi/\left(−{x}\right)} }= \\ $$$$=\int_{−{a}}…