Category: Integration

Question Number 44781 by arvinddayama01@gmail.com last updated on 04/Oct/18 $$\mathit{p}\mathit{r}\mathit{o}\mathit{v}\mathit{e}\mathit{t}\mathit{h}\mathit{a}\mathit{t}:-\int \frac{1}{\mathbf{t}\sqrt{1-{\mathbf{t}}^2}}\mathbf{dt}=\mathbf{ln}(1-\sqrt{1-{\mathbf{t}}^2})+\mathbf{C}$$ Answered by tanmay.chaudhury50@gmail.com last updated on 04/Oct/18 $$\int\frac{{tdt}}{{t}^{\mathrm{2}} \sqrt{\mathrm{1}−{t}^{\mathrm{2}} }\:} \…

Question Number 44777 by Necxx last updated on 04/Oct/18 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 110262 by Ar Brandon last updated on 28/Aug/20 $$\mathrm{Solve}\mathrm{for}\mathrm{X}(\mathrm{x},\mathrm{y},\mathrm{z}),\mathrm{Y}(\mathrm{x},\mathrm{y},\mathrm{z}),\mathrm{Z}(\mathrm{x},\mathrm{y},\mathrm{z})$$$$\{\begin{array}{l}\frac{\partial \mathrm{Z}}{\partial \mathrm{y}}-\frac{\partial \mathrm{Y}}{\partial \mathrm{z}}=1-{\mathrm{x}}^2\\ \frac{\partial \mathrm{Z}}{\partial \mathrm{x}}-\frac{\partial \mathrm{X}}{\partial \mathrm{z}}=-\frac{{\mathrm{y}}^2}{2}\\ \frac{\partial \mathrm{Y}}{\partial \mathrm{x}}-\frac{\partial \mathrm{X}}{\partial \mathrm{y}}=\mathrm{z}(2\mathrm{x}-\mathrm{y})\end{array}\mathrm{where}\{\begin{array}{l}\mathrm{X}(\mathrm{x},\mathrm{y},0)=0\\ \mathrm{Y}(\mathrm{x},\mathrm{y},0)=0\\ \mathrm{Z}(\mathrm{x},\mathrm{y},0)=0\end{array}$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 110245 by Her_Majesty last updated on 28/Aug/20 $$solve\int \frac{dx}{\sqrt[3]{c-\sqrt{b-ax}}}$$ Commented by Lordose last updated on 28/Aug/20 $$\int \frac{\mathbf{dx}}{\sqrt[3]{\mathbf{c}-\sqrt{\mathbf{b}-\mathbf{ax}}}}$$$$★\mathbf{Solution}$$$$\boldsymbol{\mathrm{set}}\:\boldsymbol{\mathrm{u}}=\boldsymbol{\mathrm{b}}−\boldsymbol{\mathrm{ax}} \…

Question Number 44706 by maxmathsup by imad last updated on 03/Oct/18 $$let{f}_{\alpha }\left(x\right)=\frac{cos\left(\alpha x\right)}{1+x^2}$$$$1)calculate{f}^{\left(n\right)}\left(x\right)and{f}^{\left(n\right)}\left(0\right)$$$$2)developpfatintegrserie$$$$\left.\mathrm{3}\right)\:{give}\:\int_{\mathrm{0}} ^{{x}} \:{f}_{\alpha} \left({t}\right)\:{dt}\:\:{at}\:{form}\:{of}\:{serie}\:…