Category: Integration

Question Number 204706 by Mummyjay last updated on 25/Feb/24 $$\mathit{e}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{a}\mathit{t}\mathit{e}{\int }_0^{\mathrm{\infty }}{2}^{-\mathbf{\Gamma }\left(\mathit{x}\right)}\mathit{d}\mathit{x}$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 204645 by cortano12 last updated on 24/Feb/24 $$\mathrm{Let}f:\left[\overline{1}\mathrm{\infty }\right)\to \mathrm{R}\mathrm{be}\mathrm{a}\mathrm{differentiable}$$$$\mathrm{function}\mathrm{such}\mathrm{that}f\left(1\right)=\frac{1}{3}\mathrm{and}$$$$3\underset{1}{\stackrel{\mathrm{x}}{\int }}f\left(t\right)dt=xf\left(x\right)-\frac{x^3}{3},\mathrm{x}\in [1,\mathrm{\infty })$$$$\mathrm{find}\mathrm{tbe}\mathrm{value}\mathrm{of}f\left(e\right)$$ Commented by universe…

Question Number 204569 by pticantor last updated on 21/Feb/24 $$\mathit{f}\mathit{i}\mathit{n}\mathit{d}\mathit{t}\mathit{h}\mathit{e}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}\mathit{o}\mathit{f}$$$$\mathit{I}={\int }_0^{+\mathrm{\infty }}\mathit{l}\mathit{n}(1+{\mathit{e}}^{-\mathit{x}})\mathit{d}\mathit{x}\mathit{n}\mathit{o}\mathit{w}\mathit{i}\mathit{n}\mathit{g}\mathit{t}\mathit{h}\mathit{a}\mathit{t}$$$$\underset{n=1}{\sum ^{+\mathrm{\infty }}}\frac{1}{{\mathit{n}}^2}=\frac{{\pi }^2}{6}$$ Answered by…

Question Number 204517 by Lindemann last updated on 20/Feb/24 Answered by witcher3 last updated on 20/Feb/24 $$\left.=\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{x}\right)\mathrm{cos}^{−\mathrm{1}} \left(\mathrm{x}\right)\right]_{−\mathrm{1}} ^{\mathrm{1}} +\int_{−\mathrm{1}} ^{\mathrm{1}} \mathrm{tan}^{−\mathrm{1}} \left(\mathrm{x}\right).\frac{\mathrm{dx}}{\:\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }}._{=\mathrm{0}}…

Question Number 204472 by mnjuly1970 last updated on 18/Feb/24 $$$$$$\mathrm{Calculate}\dots$$$$\mathrm{\Omega }=\underset{k=1}{\sum ^n}\lfloor \frac{1}{\sqrt[k]{e}-1}\rfloor =?$$$$$$ Answered by TonyCWX08 last updated…