Question Number 130448 by physicstutes last updated on 25/Jan/21 $$\mathrm{Given}\:\mathrm{that}\:{f}\left({x}\right)\:=\:{f}\left(\pi−{x}\right),\:\mathrm{prove}\:\mathrm{that}\:\int_{\mathrm{0}} ^{\pi} {xf}\left({x}\right){dx}\:=\:\frac{\pi}{\mathrm{2}}\int_{\mathrm{0}} ^{\pi} {f}\left({x}\right){dx}. \\ $$$$\mathrm{please}\:\mathrm{what}\:\mathrm{are}\:\mathrm{different}\:\mathrm{methods}\:\mathrm{to}\:\mathrm{approach}\:\mathrm{this}\:\mathrm{question}? \\ $$ Answered by TheSupreme last updated on 25/Jan/21…
Question Number 64905 by ankan0 last updated on 23/Jul/19 $$\int\mathrm{log}\:\left(\mathrm{tan}\:\mathrm{x}\right)\mathrm{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 64904 by mathmax by abdo last updated on 23/Jul/19 $${calculate}\:\int_{\mathrm{1}} ^{\mathrm{2}} \:\int_{\mathrm{0}} ^{{x}} \:\:\frac{\mathrm{1}}{\left({x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \right)^{\frac{\mathrm{3}}{\mathrm{2}}} }{dydx}\: \\ $$ Commented by ~ À…
Question Number 130432 by mnjuly1970 last updated on 25/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:{calculus}… \\ $$$$\:\:\:\:\:{calculate}\::: \\ $$$$\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\infty} {xln}\left({x}\right){e}^{−{x}} {sin}\left({x}\right){dx}=? \\ $$$$\:\:\: \\ $$ Answered by Dwaipayan Shikari…
Question Number 130433 by mnjuly1970 last updated on 25/Jan/21 $$\:\:\:\:\:\:….{nice}\:\:\:{calculus}… \\ $$$$\:\:\:{prove}\:{that}:: \\ $$$$\:\:\:\Psi=\int_{\mathrm{0}} ^{\:\infty} {e}^{−{x}} {ln}\left({x}\right){cos}\left({x}\right){dx}\overset{?} {=}\frac{\mathrm{1}}{\mathrm{8}}\left(−\mathrm{4}\gamma−\pi−\mathrm{2}{ln}\left(\mathrm{2}\right)\right) \\ $$$$ \\ $$ Answered by Dwaipayan…
Question Number 130431 by mnjuly1970 last updated on 25/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{nice}\:\:\:{calculus}… \\ $$$$\:{please}\:\:{evaluate}\::: \\ $$$$\:\:\:\phi=\int_{\mathrm{0}} ^{\:\infty} {tanh}\left({x}\right).{e}^{−{sx}} {dx}=?? \\ $$$$\:\:\:\:\:\:\:\left(\:\:{s}>\mathrm{0}\:\:\:{and}\:\:\:{real}…\right) \\ $$ Answered by Dwaipayan Shikari…
Question Number 130417 by Lordose last updated on 25/Jan/21 $$\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{sin}\left(\alpha\mathrm{x}\right)\mathrm{sin}\left(\beta\mathrm{x}\right)}{\mathrm{x}^{\mathrm{2}} }\mathrm{dx} \\ $$ Answered by mathmax by abdo last updated on 25/Jan/21 $$\mathrm{I}\:=\int_{\mathrm{0}}…
Question Number 64873 by mathmax by abdo last updated on 22/Jul/19 $${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\pi} \:\:\frac{{dt}}{{x}+{sint}}\:\:\:{with}\:{xreal} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{also}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\pi} \:\:\frac{{dt}}{\left({x}+{sint}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right)\:{give}\:{f}^{\left({n}\right)} \left({x}\right)\:{at}\:{form}\:{of}\:{integral} \\…
Question Number 130402 by pipin last updated on 25/Jan/21 $$\: \\ $$$$\:\int\:\left(\boldsymbol{\mathrm{e}}^{\boldsymbol{\mathrm{x}}} \right).\left(\frac{\boldsymbol{\mathrm{x}}^{\mathrm{6}} +\boldsymbol{\mathrm{x}}^{\mathrm{5}} +\mathrm{5}\boldsymbol{\mathrm{x}}^{\mathrm{4}} }{\left(\mathrm{1}+\boldsymbol{\mathrm{x}}\right)^{\mathrm{6}} }\right)\boldsymbol{\mathrm{dx}}\:=\:… \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 64866 by mathmax by abdo last updated on 22/Jul/19 $${find}\:\int_{\mathrm{1}} ^{+\infty} \:\frac{{dx}}{{x}^{\mathrm{2}} \sqrt{\mathrm{1}+{x}+{x}^{\mathrm{2}} }} \\ $$ Commented by mathmax by abdo last updated…