Question Number 72466 by Learner-123 last updated on 29/Oct/19 $${Prove}\:{that}\:\int_{\mathrm{0}} ^{\:\mathrm{2}} \int_{−\sqrt{\mathrm{1}−\left({y}−\mathrm{1}\right)^{\mathrm{2}} }} ^{\:\:\mathrm{0}\:} \:{xy}^{\mathrm{2}} {dxdy}\:=\:−\frac{\mathrm{4}}{\mathrm{5}} \\ $$$$\boldsymbol{{after}}\:\mathrm{changing}\:\mathrm{the}\:\mathrm{integral}\:\mathrm{to}\:\boldsymbol{\mathrm{polar}}\:\boldsymbol{\mathrm{form}}. \\ $$ Commented by Abdo msup. last…
Question Number 137991 by EnterUsername last updated on 08/Apr/21 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}^{\mathrm{3}} \left({sinx}\right){dx} \\ $$ Answered by Ar Brandon last updated on 08/Apr/21 $$\mathrm{f}\left(\alpha\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}}…
Question Number 72445 by aliesam last updated on 28/Oct/19 $$\int\frac{{x}\:{cos}\left({ax}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 137973 by mnjuly1970 last updated on 08/Apr/21 $$\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:…….{Advanced}\:…\:…\:…\:…\:{Calculus}……. \\ $$$$\:\:\:\:{prove}\:{that}::: \\ $$$$\:\:\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}\left(\mathrm{1}−{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx}=\frac{\pi}{\mathrm{8}}{ln}\left(\mathrm{2}\right)−{G}\:…\checkmark \\ $$$$\:\:\:\:{where}\:\:{G}\:{is}\:{catalan}\:{number}… \\ $$$$\:\:\: \\ $$…
Question Number 137969 by rs4089 last updated on 08/Apr/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }{dx}\:{dy} \\ $$ Answered by EnterUsername last updated on 08/Apr/21…
Question Number 137971 by EnterUsername last updated on 08/Apr/21 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}: \\ $$$$\int_{\mathrm{0}} ^{\mathrm{x}} \left(\mathrm{x}−\mathrm{t}\right)\mathrm{t}^{\mathrm{2}} \sqrt[{\mathrm{3}}]{\mathrm{y}\left(\mathrm{t}\right)}\mathrm{dt}+\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{0}} ^{\mathrm{x}} \left(\mathrm{5x}−\mathrm{6t}\right)\mathrm{y}\left(\mathrm{t}\right)\mathrm{dt}+\mathrm{2x}=\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 137953 by mnjuly1970 last updated on 08/Apr/21 $$\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:….\mathscr{N}{ice}\:…\:…\:…\:…\mathscr{C}{alculus}…. \\ $$$$\:\:\:\:\:{find}\:\:{the}\:{value}\:{of}:: \\ $$$$\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{1}} ^{\:\infty} \frac{{ln}\left(\mathrm{1}+{x}\right)}{{x}^{\mathrm{2}} }{dx}=??? \\ $$ Answered by Ñï= last…
Question Number 137940 by benjo_mathlover last updated on 08/Apr/21 $$\int_{\mathrm{1}} ^{\:{e}} \sqrt{\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{2}} }+\frac{\mathrm{1}}{\left({x}+\mathrm{1}\right)^{\mathrm{2}\:} }}\:{dx}\:=? \\ $$ Answered by john_santu last updated on 08/Apr/21 $$\mathcal{J}\:=\:\int_{\mathrm{1}} ^{\:{e}}…
Question Number 137937 by benjo_mathlover last updated on 08/Apr/21 $$\:\underset{−\infty} {\overset{\:\:\:\infty} {\int}}\frac{\mathrm{ln}\left(\:\mid{x}\mid\right)}{\left({x}^{\mathrm{2}} +{a}^{\mathrm{2}} \right)^{\mathrm{2}} }\:{dx}\:=? \\ $$ Answered by Ñï= last updated on 14/Apr/21 $$\int_{−\infty}…
Question Number 6865 by Tawakalitu. last updated on 31/Jul/16 $$\int\frac{{sin}\left({x}\right)\:+\:{cos}\left({x}\right)}{{e}^{−{x}} \:+\:{sin}\left({x}\right)}\:{dx} \\ $$ Commented by Yozzii last updated on 31/Jul/16 $${sinhix}={isinx} \\ $$$${sinx}=\frac{{sinhix}}{{i}}=\frac{{e}^{{ix}} −{e}^{−{ix}} }{\mathrm{2}{i}}…