Question Number 65478 by smz last updated on 30/Jul/19 Commented by MJS last updated on 31/Jul/19 $$\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{think}\:\mathrm{it}'\mathrm{s}\:\mathrm{possible} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 65455 by mathmax by abdo last updated on 30/Jul/19 $${find}\:{U}_{{n}} =\:\int_{\mathrm{0}} ^{+\infty} \:\:\:\frac{\left(−\mathrm{1}\right)^{{x}} }{\mathrm{2}^{{x}^{\mathrm{2}} } \left({x}^{\mathrm{2}} \:+\mathrm{4}{n}^{\mathrm{2}} \right)}{dx}\:\:\:\:\:\left({n}\:{from}\:{N}\:{and}\:{n}\geqslant\mathrm{1}\right) \\ $$$${study}\:{nature}\:{of}\:{the}\:{serie}\:\:\Sigma\:\mathrm{2}^{{n}^{\mathrm{2}} } {U}_{{n}} \\…
Question Number 65450 by imron876 last updated on 30/Jul/19 Commented by Prithwish sen last updated on 30/Jul/19 $$\left.\mathrm{1}\right)\:\mathrm{a}=\mathrm{b}=\mathrm{c}=\mathrm{d}=\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\mathrm{a}=\mathrm{c}=\mathrm{1},\mathrm{b}=\mathrm{d}=\mathrm{0} \\ $$$$\left.\mathrm{3}\right)\mathrm{b}=\mathrm{d}=\mathrm{1},\mathrm{a}=\mathrm{c}=\mathrm{0} \\ $$$$\left.\mathrm{4}\right)\mathrm{a}=\mathrm{1}\:\mathrm{c}=−\mathrm{1}\:\mathrm{b}=\mathrm{d}=\mathrm{0} \\…
Question Number 65445 by mathmax by abdo last updated on 30/Jul/19 $${find}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {ln}\left({cost}\:+{xsint}\right){dt}\:\:\: \\ $$ Commented by Prithwish sen last updated on 30/Jul/19 $$\mathrm{f}\left(\mathrm{x}\right)\:=\:\frac{\pi−\mathrm{2}\sqrt{\mathrm{2}}}{\mathrm{8}}\:\mathrm{ln}\mid\mathrm{1}+\mathrm{x}^{\mathrm{2}}…
Question Number 130979 by mnjuly1970 last updated on 31/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\phi\:=\int_{\mathrm{0}} ^{\:\infty} {log}^{\mathrm{2}} \left({x}\right){sin}\left({x}^{\mathrm{2}} \right){dx}=? \\ $$$$\:\:\:\:\:{i}\:{had}\:{solved}\:{that}\:{already}\:\:{and}: \\ $$$$\:\:\:{answ}\:\::\:=\:−\frac{\pi^{\mathrm{2}} \sqrt{\mathrm{2}\pi}\:}{\mathrm{32}} \\ $$$$\:\:\:\:\: \\ $$$$\:\:\:…
Question Number 65443 by imron876 last updated on 30/Jul/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 130958 by bramlexs22 last updated on 31/Jan/21 $$\:\int_{\:\mathrm{0}} ^{\:\pi/\mathrm{2}} \:\frac{{x}}{\mathrm{sec}\:{x}+\mathrm{csc}\:{x}}\:{dx} \\ $$ Commented by benjo_mathlover last updated on 31/Jan/21 $$\mathrm{M}\:=\:\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\frac{\mathrm{x}}{\mathrm{sec}\:\mathrm{x}+\mathrm{csc}\:\mathrm{x}}\:\mathrm{dx}\:=\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}}…
Question Number 65420 by imron876 last updated on 29/Jul/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 65400 by mathmax by abdo last updated on 29/Jul/19 $${find}\:{f}\left(\alpha\right)\:=\int_{\mathrm{1}} ^{+\infty} \:\frac{{arctan}\left(\frac{\alpha}{{x}}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx}\:\:\:\:{with}\:\alpha\geqslant\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 65401 by mathmax by abdo last updated on 29/Jul/19 $${let}\:{f}\left({x},{y}\right)=\left({x}+{y}\right)\sqrt{{x}+{y}−\mathrm{1}} \\ $$$${calculate}\:\:\int\int_{{D}} {f}\left({x},{y}\right){dxdy}\:{with}\: \\ $$$${D}\:=\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /\:\:\mathrm{1}\leqslant{x}\leqslant\mathrm{2}\:\:{and}\:\:\:\mathrm{1}\leqslant{y}\leqslant\sqrt{\mathrm{3}}\right\} \\ $$ Commented by mathmax by abdo…