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Category: Integration

prove-that-1-t-1-t-2-dt-ln-1-1-t-2-C-

Question Number 44781 by arvinddayama01@gmail.com last updated on 04/Oct/18 $$\boldsymbol{{prove}}\:\boldsymbol{{that}}:−\:\int\frac{\mathrm{1}}{\boldsymbol{\mathrm{t}}\sqrt{\mathrm{1}−\boldsymbol{\mathrm{t}}^{\mathrm{2}} }}\boldsymbol{\mathrm{dt}}\:=\:\boldsymbol{\mathrm{ln}}\left(\mathrm{1}−\sqrt{\mathrm{1}−\boldsymbol{\mathrm{t}}^{\mathrm{2}} }\right)+\boldsymbol{\mathrm{C}} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 04/Oct/18 $$\int\frac{{tdt}}{{t}^{\mathrm{2}} \sqrt{\mathrm{1}−{t}^{\mathrm{2}} }\:} \\…

Solve-for-X-x-y-z-Y-x-y-z-Z-x-y-z-Z-y-Y-z-1-x-2-Z-x-X-z-y-2-2-Y-x-X-y-z-2x-y-where-X-x-y-0-0-Y-x-y-0-0-Z-x-y-0-0-

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

Question-44712

Question Number 44712 by peter frank last updated on 03/Oct/18 Answered by tanmay.chaudhury50@gmail.com last updated on 03/Oct/18 $$\left.\mathrm{1}\right)\int\frac{{x}^{{n}−\mathrm{1}} }{{x}^{{n}} \left(\mathrm{1}+{x}^{{n}} \right)}{dx} \\ $$$${t}={x}^{{n}} \:\:\:{dt}={nx}^{{n}−\mathrm{1}} {dx}…

solve-dx-c-b-ax-1-3-

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

let-f-x-cos-x-1-x-2-1-calculate-f-n-x-and-f-n-0-2-developp-f-at-integr-serie-3-give-0-x-f-t-dt-at-form-of-serie-4-developp-0-f-t-dt-at-integr-se

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