Category: Integration

Question Number 199903 by frankpenredpen last updated on 11/Nov/23 $$\int \frac{x^{2}dx}{\sqrt{x^2-16}}=?$$ Commented by cortano12 last updated on 11/Nov/23 $$\mathrm{why}\partial \mathrm{x}?$$ Answered…

Question Number 199570 by universe last updated on 05/Nov/23 $$\mathrm{I}={\int }_0^{\pi /2}{\tan }^{-1}\left(\frac{\sin x}{2}\right)dx$$ Answered by witcher3 last updated on 05/Nov/23 $$\mathrm{I}\left(\mathrm{a}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{tan}^{−\mathrm{1}}…

Question Number 199468 by Calculusboy last updated on 04/Nov/23 Answered by witcher3 last updated on 04/Nov/23 $$\frac{\mathrm{x}}{2021\pi }\iff$$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}}{\mathrm{e}^{\mathrm{t}^{\mathrm{2021}} } }\left(\mathrm{1}+\mathrm{t}^{\mathrm{2022}} \right)^{\frac{\mathrm{1}}{\mathrm{2022}}} \mathrm{dt}=\mathrm{I}…

Question Number 199377 by universe last updated on 02/Nov/23 $$\int \underset{\mathrm{R}}{\int }\cos \left(\max \{{\mathrm{x}}^3,{\mathrm{y}}^{3/2}\}\right)\mathrm{dx}\mathrm{dy},\mathrm{where}\mathrm{R}=[0,1]\times [0,1]$$ Answered by witcher3 last updated on 04/Nov/23 $$\mathrm{i}\mathrm{will}\mathrm{Try}$$…

Question Number 199213 by emilagazade last updated on 29/Oct/23 Answered by witcher3 last updated on 29/Oct/23 $${\int }_{\mathrm{a}}^{\mathrm{b}}(\mathrm{x}-\left[\mathrm{x}\right]-\frac{1}{2}){\mathrm{f}}^{\prime }\left(\mathrm{x}\right)=\mathrm{dx}$$$$=\underset{\mathrm{k}=\mathrm{a}} {\overset{\mathrm{b}−\mathrm{1}} {\sum}}\int_{\mathrm{k}} ^{\mathrm{k}+\mathrm{1}} \left(\mathrm{x}−\left[\mathrm{x}\right]−\frac{\mathrm{1}}{\mathrm{2}}\right)\mathrm{f}'\left(\mathrm{x}\right)\mathrm{dx}…