Question Number 119591 by Lordose last updated on 25/Oct/20 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:{calculus}… \\ $$$$\:\:\:{prove}\:\:{that}\::: \\ $$$$ \\ $$$$\:\: \\ $$$$\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \sqrt{\frac{\left(\mathrm{2}^{{x}} −\mathrm{1}\right){sin}^{\mathrm{3}} \left({x}\right)}{\left(\mathrm{2}^{{x}} +\mathrm{1}\right)\left({sin}^{\mathrm{3}}…
Question Number 119570 by mnjuly1970 last updated on 25/Oct/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:\underset{\clubsuit} {\overset{\clubsuit} {\clubsuit}}{nice}\:\:{calculus}\underset{\clubsuit} {\overset{\clubsuit} {\clubsuit}}… \\ $$$$\:\:\:\:{prove}\:{that}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\infty} {e}^{−\mathrm{2}{x}} {ln}\left(\frac{\mathrm{1}+{e}^{−{x}} }{\mathrm{1}−{e}^{−{x}} }\right)=\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\bigstar\:\mathscr{M}.\mathscr{N}.\mathrm{1970}\bigstar……
Question Number 185104 by emmanuelson123 last updated on 17/Jan/23 Answered by aba last updated on 17/Jan/23 $$\pi\mathrm{ln}\left(\mathrm{6}+\mathrm{4}\sqrt{\mathrm{2}}\right) \\ $$ Commented by emmanuelson123 last updated on…
Question Number 54011 by maxmathsup by imad last updated on 27/Jan/19 $${calculate}\:{f}\left({a}\right)\:=\int\:\:\:\:\frac{{dx}}{\:\sqrt{\mathrm{1}+{ax}}−\sqrt{\mathrm{1}−{ax}}}\:\:{with}\:{a}>\mathrm{0}\:. \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:{U}_{{n}} =\int_{−\frac{\mathrm{1}}{{na}}} ^{\frac{\mathrm{1}}{{na}}} \:\:\frac{{dx}}{\:\sqrt{\mathrm{1}+{ax}}−\sqrt{\mathrm{1}−{ax}}}\:\:{with}\:{n}\:{from}\:{N}\:{and}\:{n}>\mathrm{1} \\ $$$${find}\:{lim}_{{n}\rightarrow+\infty} \:{U}_{{n}} \:\:\:{and}\:{study}\:{the}\:{convergence}\:{of}\:\Sigma\:{U}_{{n}} \\ $$ Commented by…
Question Number 185058 by saboorhalimi last updated on 16/Jan/23 Answered by Frix last updated on 16/Jan/23 $${k}\mathrm{cos}\:{nx}\:+{m}\mathrm{sin}\:{nx}\:=\sqrt{{k}^{\mathrm{2}} +{m}^{\mathrm{2}} }\mathrm{sin}\:\left({nx}+\mathrm{tan}^{−\mathrm{1}} \:\frac{{k}}{{m}}\right) \\ $$$$\Omega=\sqrt{{k}^{\mathrm{2}} +{m}^{\mathrm{2}} }\underset{\mathrm{0}} {\overset{\pi}…
Question Number 53967 by maxmathsup by imad last updated on 27/Jan/19 $$\left.\mathrm{1}\right){calculate}\:{A}_{{t}} =\int_{\mathrm{0}} ^{\infty} \:{e}^{−{xt}} \:{sinxdx}\:\:{with}\:{x}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:{by}\:{using}\:{Fubuni}\:{theorem}\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{sinx}}{{x}}{dx}\:. \\ $$ Commented by maxmathsup…
Question Number 53966 by maxmathsup by imad last updated on 27/Jan/19 $${let}\:{f}\left({x}\right)\:={xsinx}\:,\mathrm{2}\pi\:{periodic}\:{even} \\ $$$${developp}\:{f}\:{at}\:{Fourier}\:{serie}\:. \\ $$ Commented by maxmathsup by imad last updated on 30/Jan/19…
Question Number 53963 by maxmathsup by imad last updated on 27/Jan/19 $${let}\:{f}\left({x}\right)\:=\:{x}\mid{x}\mid\:\:\:,\:\mathrm{2}\pi\:{periodic}\:\:{odd}\: \\ $$$${developp}\:{f}\:{at}\:{fourier}\:{serie}\:. \\ $$ Commented by maxmathsup by imad last updated on 31/Jan/19…
Question Number 53958 by maxmathsup by imad last updated on 27/Jan/19 $${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left({x}\right){ln}\left(\mathrm{1}−{x}^{\mathrm{2}} \right){dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 53956 by maxmathsup by imad last updated on 27/Jan/19 $${give}\int_{\mathrm{0}} ^{\mathrm{1}} \:{e}^{−{x}} {ln}\left(\mathrm{1}−{x}\right){dx}\:\:{at}\:{form}\:{of}\:{serie} \\ $$ Commented by maxmathsup by imad last updated on…