Question Number 133183 by bounhome last updated on 19/Feb/21 $$\int\sqrt{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{3}} }{dx}=…? \\ $$ Answered by physicstutes last updated on 19/Feb/21 $$\mathrm{let}\:{x}\:=\:\mathrm{sinh}\:\theta\:\Rightarrow\:{dx}\:=\:\mathrm{cosh}\:\theta\:{d}\theta \\ $$$$\mathrm{now},\:\int\sqrt{\left[\left(\mathrm{sinh}\:\theta\right)^{\mathrm{2}} +\mathrm{1}\right]^{\mathrm{3}}…
Question Number 133179 by abdullahquwatan last updated on 19/Feb/21 $$\mathrm{given}\:\mathrm{that}\:\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{mx}^{\mathrm{2}} +\mathrm{4}\sqrt{\mathrm{3}}\mathrm{x}+\mathrm{n}}{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\:\mathrm{and}\:\mathrm{f}\:\mathrm{max}=\mathrm{7} \\ $$$$\mathrm{f}\:\mathrm{min}=−\mathrm{1}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{m}\:\mathrm{and}\:\mathrm{n} \\ $$ Commented by abdullahquwatan last updated on 20/Feb/21 $$\mathrm{thx} \\…
Question Number 133173 by john_santu last updated on 19/Feb/21 $$\int_{\mathrm{0}} ^{\:\frac{\mathrm{1}}{\mathrm{2}}} \:\sqrt{\mathrm{1}+\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }}\:\mathrm{dx}\:=? \\ $$ Answered by EDWIN88 last updated on 19/Feb/21 $$\mathrm{I}=\int_{\mathrm{0}} ^{\:\frac{\mathrm{1}}{\mathrm{2}}} \sqrt{\mathrm{1}+\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}}…
Question Number 2103 by Yozzi last updated on 02/Nov/15 $${Find}\:{the}\:{integral} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\frac{{dx}}{{x}^{\mathrm{4}} −{x}^{\mathrm{2}} +\mathrm{1}}. \\ $$ Commented by Yozzi last updated on 02/Nov/15 $${Yup}. \\…
Question Number 133168 by bemath last updated on 19/Feb/21 Answered by floor(10²Eta[1]) last updated on 19/Feb/21 $$\mathrm{x}\rightarrow\mathrm{1}−\frac{\mathrm{1}}{\mathrm{x}} \\ $$$$\left(\mathrm{I}\right):\:\mathrm{f}\left(\frac{\mathrm{x}}{\mathrm{x}−\mathrm{1}}\right)+\mathrm{f}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)=\frac{\mathrm{x}−\mathrm{1}}{\mathrm{x}} \\ $$$$\mathrm{but}\:\mathrm{f}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)=\mathrm{x}−\mathrm{f}\left(\mathrm{1}−\mathrm{x}\right),\:\mathrm{so} \\ $$$$\mathrm{f}\left(\frac{\mathrm{x}}{\mathrm{x}−\mathrm{1}}\right)+\mathrm{x}−\mathrm{f}\left(\mathrm{1}−\mathrm{x}\right)=\frac{\mathrm{x}−\mathrm{1}}{\mathrm{x}} \\ $$$$\left(\mathrm{II}\right):\:\mathrm{f}\left(\frac{\mathrm{x}}{\mathrm{x}−\mathrm{1}}\right)−\mathrm{f}\left(\mathrm{1}−\mathrm{x}\right)=\frac{−\mathrm{x}^{\mathrm{2}}…
Question Number 67631 by Hassen_Timol last updated on 29/Aug/19 $$ \\ $$$$ \\ $$$$\:\:\:\mathrm{Can}\:\mathrm{you}\:\mathrm{please}\:\mathrm{tell}\:\mathrm{me},\:\mathrm{where}\:\mathrm{does}\:\mathrm{this}\: \\ $$$$\:\:\:\mathrm{formula}\:\mathrm{come}\:\mathrm{from}? \\ $$$$\:\:\:\mathrm{And}\:\mathrm{what}\:\mathrm{means}\:\mathrm{the}\:\mathrm{factorial}\:\mathrm{of}\:\mathrm{a}\:\mathrm{non}- \\ $$$$\:\:\:\mathrm{integer}\:\mathrm{number}? \\ $$$$ \\ $$$$\:\:\:\:\:\:\pi\:=\:\left(\frac{\mathrm{1}}{\mathrm{2}}!\right)^{\mathrm{2}} ×\:\mathrm{4}…
Question Number 67628 by mhmd last updated on 29/Aug/19 $$\int{x}^{{n}} {lnx}/{n}^{{x}\:} \:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 2092 by Filup last updated on 02/Nov/15 $$\mathrm{If}\:\boldsymbol{{A}}=\langle{p}_{{x}} ,\:{p}_{{y}} ,\:{p}_{{z}} \rangle\:\mathrm{is}\:\mathrm{a}\:\mathrm{position}\:\mathrm{vector}\: \\ $$$$\mathrm{in}\:\mathrm{standard}\:\mathrm{position},\:\mathrm{vector}\:\boldsymbol{{r}}=\langle{r}_{{x}} ,\:{r}_{{y}} ,\:{r}_{{z}} \rangle \\ $$$$\mathrm{is}\:\mathrm{the}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{a}\:\mathrm{3}\:\mathrm{dimensional}\:\mathrm{circle} \\ $$$$\mathrm{with}\:\mathrm{focal}\:\mathrm{point}\:\mathrm{at}\:\boldsymbol{{A}},\:\mathrm{Solve}\:\mathrm{for}\:\mathrm{the} \\ $$$$\mathrm{vector}\:\mathrm{equation}\:\boldsymbol{{r}}\left(\theta\right)\:\mathrm{such}\:\mathrm{that}\:\mathrm{it}\:\mathrm{is}\:\mathrm{the} \\…
Question Number 133161 by abdullahquwatan last updated on 19/Feb/21 $$\mathrm{give}\:\mathrm{me}\:\mathrm{problems}\:\mathrm{algebra}\:\mathrm{limit}\:\mathrm{function}\:\mathrm{hard} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 2089 by Yozzi last updated on 01/Nov/15 $${If}\:{x}\in\left[\mathrm{0},\mathrm{0}.\mathrm{5}\pi\right],\:{show}\:{that}\:{sinx}\geqslant{x}−\frac{\mathrm{1}}{\mathrm{6}}{x}^{\mathrm{3}} . \\ $$$${Hence}\:{prove}\:{that} \\ $$$$\frac{\mathrm{1}}{\mathrm{3000}}\leqslant\int_{\mathrm{0}} ^{\mathrm{1}/\mathrm{10}} \frac{{x}^{\mathrm{2}} }{\left(\mathrm{1}−{x}+{sinx}\right)^{\mathrm{2}} }{dx}\leqslant\frac{\mathrm{2}}{\mathrm{5999}}. \\ $$ Commented by prakash jain…