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Category: Integration

1-0-pi-2-x-2-sin-2-x-dx-1-2-2-0-pi-2-x-tan-x-

Question Number 195846 by mnjuly1970 last updated on 11/Aug/23 $$ \\ $$$$\:\:\:\:\:\:\begin{cases}{\:\:\:\Omega_{\mathrm{1}} \:=\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{\:{x}^{\:\mathrm{2}} }{{sin}^{\:\mathrm{2}} \left({x}\right)}\:{dx}\:}\\{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:\:\:\frac{\Omega_{\mathrm{1}} }{\Omega_{\:\mathrm{2}} }\:=\:?\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}\\{\:\:\Omega_{\:\mathrm{2}} =\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{{x}}{{tan}\left({x}\right)}\:{dx}}\end{cases} \\ $$$$ \\…

Soit-f-n-x-2-n-1-1-2-n-cotan-x-2-n-cotanx-sin-x-2-n-Calculer-lim-x-0-f-n-x-et-lim-n-f-n-x-2-2n-2-

Question Number 195126 by Erico last updated on 25/Jul/23 $$\mathrm{Soit}\:{f}_{{n}} \left({x}\right)=\mathrm{2}^{{n}+\mathrm{1}} \left[\frac{\frac{\mathrm{1}}{\mathrm{2}^{{n}} }{cotan}\left(\frac{{x}}{\mathrm{2}^{{n}} }\right)−{cotanx}}{{sin}\left(\frac{{x}}{\mathrm{2}^{{n}} }\right)}\right] \\ $$$${Calculer}\:\underset{{x}\rightarrow\mathrm{0}} {{lim}f}_{{n}} \left({x}\right)\:{et}\:\underset{{n}\rightarrow+\infty} {{lim}}\:\frac{{f}_{{n}} \left({x}\right)}{\mathrm{2}^{\mathrm{2}{n}+\mathrm{2}} } \\ $$ Answered…

1-x-5-1-dx-

Question Number 194975 by youssef last updated on 21/Jul/23 $$\int\frac{\mathrm{1}}{\boldsymbol{{x}}^{\mathrm{5}} +\mathrm{1}}\boldsymbol{{dx}} \\ $$ Commented by Frix last updated on 21/Jul/23 $$\mathrm{You}\:\mathrm{have}\:\mathrm{to}\:\mathrm{decompose} \\ $$$${x}^{\mathrm{5}} +\mathrm{1}=\left({x}+\mathrm{1}\right)\left({x}^{\mathrm{2}} −\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}{x}+\mathrm{1}\right)\left({x}^{\mathrm{2}}…

Question-194963

Question Number 194963 by C2coder last updated on 20/Jul/23 Answered by witcher3 last updated on 21/Jul/23 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{2asin}\left(\mathrm{x}\right)}{\mathrm{1}−\mathrm{a}^{\mathrm{2}} \mathrm{sin}^{\mathrm{2}} \left(\mathrm{x}\right)}\right)\mathrm{dx}..? \\ $$$$ \\…