Question Number 67138 by mhmd last updated on 23/Aug/19 $${find}\:{the}\:{area}\:{abounded}\:{y}=\sqrt{{x}} \\ $$$${and}\:{y}={x}−\mathrm{2}? \\ $$ Commented by mr W last updated on 23/Aug/19 $${sir}:\:{you}\:{don}'{t}\:{need}\:{to}\:{repeat}\:{the} \\ $$$${same}\:{question}\:{so}\:{frequently}.…
Question Number 1602 by 112358 last updated on 25/Aug/15 $${Show}\:{that}\: \\ $$$$\frac{{d}}{{dy}}\int_{{g}_{\mathrm{1}} \left({y}\right)} ^{{g}_{\mathrm{2}} \left({y}\right)} {f}\left({x},{y}\right){dx}=\int_{{g}_{\mathrm{1}} \left({y}\right)} ^{{g}_{\mathrm{2}} \left({y}\right)} \frac{\partial{f}}{\partial{y}}\left({x},{y}\right){dx}+{g}_{\mathrm{2}} ^{'} \left({y}\right){f}\left({g}_{\mathrm{2}} \left({y}\right),{y}\right)−{g}_{\mathrm{1}} ^{'} \left({y}\right){f}\left({g}_{\mathrm{1}}…
Question Number 1582 by 112358 last updated on 21/Aug/15 $${Let}\:\phi\:{and}\:\varepsilon\:{denote}\:{functions}\:{of}\:{x} \\ $$$${where}\:\phi\:{is}\:{odd}\:{and}\:\varepsilon\:{is}\:{even}\:\forall{x}\in\mathbb{R}. \\ $$$${Is}\:{it}\:{generally}\:{true}\:{that}\:{integrating} \\ $$$${an}\:{odd}\:{function}\:{gives}\:{an}\:{even} \\ $$$${function}\:{and}\:{vice}\:{versa}?\: \\ $$$$\int\phi_{\mathrm{1}} \left({x}\right)\:{dx}=\varepsilon_{\mathrm{1}} \left({x}\right)+{C}\:? \\ $$$${and}\:\int\phi_{\mathrm{2}} \left({x}\right){dx}=\varepsilon_{\mathrm{2}}…
Question Number 67106 by mhmd last updated on 22/Aug/19 $${find}\:{the}\:{area}\:{abounded}\:{y}=\sqrt{{x}} \\ $$$${afind}\:{y}={x}−\mathrm{2}? \\ $$ Commented by kaivan.ahmadi last updated on 24/Aug/19 $${x}−\mathrm{2}=\sqrt{{x}}\Rightarrow{x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{4}=\mathrm{0}\Rightarrow\left({x}−\mathrm{1}\right)\left({x}−\mathrm{4}\right)=\mathrm{0}\Rightarrow \\ $$$$\begin{cases}{{x}=\mathrm{1}}\\{{x}=\mathrm{2}}\end{cases}…
Question Number 67105 by mhmd last updated on 22/Aug/19 $${find}\:{the}\:{area}\:{abounded}\:{y}=\sqrt{{x}} \\ $$$${afind}\:{y}={x}−\mathrm{2}? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 132610 by liberty last updated on 15/Feb/21 $$\Omega=\int\:\frac{\mathrm{sin}\:^{\mathrm{2}} \left(\mathrm{x}\right)}{\mathrm{1}+\mathrm{sin}\:^{\mathrm{2}} \left(\mathrm{x}\right)}\:\mathrm{dx}\: \\ $$ Answered by Dwaipayan Shikari last updated on 15/Feb/21 $$\int\frac{{sin}^{\mathrm{2}} {x}}{\mathrm{1}+{sin}^{\mathrm{2}} {x}}{dx}={x}−\int\frac{\mathrm{1}}{\mathrm{1}+{sin}^{\mathrm{2}}…
Question Number 67070 by mRDv143 last updated on 22/Aug/19 Commented by Prithwish sen last updated on 23/Aug/19 $$\int\frac{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} \:\sqrt{\mathrm{x}^{\mathrm{3}} +\mathrm{x}^{\mathrm{2}} +\mathrm{x}}}\:\mathrm{dx}=\int\frac{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} .\mathrm{x}\:\sqrt{\mathrm{x}+\frac{\mathrm{1}}{\mathrm{x}}+\mathrm{1}}}\:\mathrm{dx} \\…
Question Number 132600 by Ahmed1hamouda last updated on 15/Feb/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 67069 by mRDv143 last updated on 22/Aug/19 Commented by Prithwish sen last updated on 22/Aug/19 $$\int\frac{\left(\mathrm{1}+\mathrm{logx}\right)^{\mathrm{2}} }{\mathrm{1}+\mathrm{xlogx}+\mathrm{logx}+\mathrm{x}\left(\mathrm{logx}\right)^{\mathrm{2}} }\:\mathrm{dx} \\ $$$$=\:\int\frac{\left(\mathrm{1}+\mathrm{logx}\right)^{\mathrm{2}} }{\left(\mathrm{1}+\mathrm{logx}\right)\left(\mathrm{1}+\mathrm{xlogx}\right)}\:\mathrm{dx} \\ $$$$=\int\frac{\mathrm{1}+\mathrm{logx}}{\mathrm{1}+\mathrm{xlogx}}\:\mathrm{dx}\:\:\mathrm{put}\:\mathrm{1}+\mathrm{xlogx}\:=\:\mathrm{u}\Rightarrow\left(\mathrm{1}+\mathrm{logx}\right)\mathrm{dx}=\:\mathrm{du}…
Question Number 132598 by Ahmed1hamouda last updated on 15/Feb/21 $$ \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{voloume}\:\mathrm{bounded}\:\mathrm{by}\:\mathrm{z}=\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} } \\ $$$$\mathrm{and}\:\mathrm{the}\:\mathrm{plane}\:\mathrm{y}+\mathrm{z}=\mathrm{3} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com