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…
Question Number 65398 by mathmax by abdo last updated on 29/Jul/19 $$\left.\mathrm{1}\right)\:{calculate}\:\:{A}_{{n}} =\int\int_{\left[\mathrm{1},{n}\left[^{\mathrm{2}} \right.\right.} \:\:\:\:\:{sin}\left({x}^{\mathrm{2}} \:+\mathrm{3}{y}^{\mathrm{2}} \right)\:{e}^{−{x}^{\mathrm{2}} −\mathrm{3}{y}^{\mathrm{2}} } {dxdy} \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \\ $$…
Question Number 65399 by mathmax by abdo last updated on 29/Jul/19 $$\left.\mathrm{1}\right)\:{calculate}\:{A}_{{n}} =\:\int\int_{\left[\mathrm{0},{n}\left[^{\mathrm{2}} \right.\right.} \:\:\:\frac{{dxdy}}{\:\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +\mathrm{4}}} \\ $$$$\left.\mathrm{2}\right){find}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \\ $$ Commented by mathmax…
Question Number 65395 by imron876 last updated on 29/Jul/19 Commented by mathmax by abdo last updated on 29/Jul/19 $$\int\:\left(−\mathrm{1}\right)^{{x}} {dx}\:=\int\:{e}^{{i}\pi{x}} {dx}\:=\frac{\mathrm{1}}{{i}\pi}{e}^{{i}\pi{x}} \:+{c}\:=\frac{\left(−\mathrm{1}\right)^{{x}} }{{i}\pi}\:+{c} \\ $$…