Question Number 129868 by Bird last updated on 20/Jan/21 $${find}\:{lim}_{{n}\rightarrow+\infty} \frac{\mathrm{1}}{{n}}\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:\frac{{k}}{\:\sqrt{\mathrm{4}{n}^{\mathrm{2}} −{k}^{\mathrm{2}} }} \\ $$ Answered by Ar Brandon last updated on 20/Jan/21…
Question Number 129867 by Bird last updated on 20/Jan/21 $${calculate}\:\int\:\:\:\frac{\mathrm{2}{x}−\mathrm{1}}{\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)^{\mathrm{3}} }{dx} \\ $$ Answered by Olaf last updated on 20/Jan/21 $$\Omega\:=\:\int\frac{\mathrm{2}{x}−\mathrm{1}}{\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)^{\mathrm{3}} }{dx}\:=\:\int\frac{{du}}{{u}^{\mathrm{3}} }…
Question Number 129859 by EDWIN88 last updated on 20/Jan/21 $$\:\mathrm{L}\:=\:\int_{−\mathrm{1}} ^{\:\mathrm{0}} \sqrt{\frac{\mathrm{1}+\mathrm{y}}{\mathrm{1}−\mathrm{y}}}\:\mathrm{dy}\: \\ $$ Answered by liberty last updated on 20/Jan/21 $$\:\mathrm{let}\:\mathrm{y}=\mathrm{cos}\:\mathrm{2t}\:\rightarrow\begin{cases}{\mathrm{y}=\mathrm{0}\rightarrow\mathrm{t}=\frac{\pi}{\mathrm{4}}}\\{\mathrm{y}=−\mathrm{1}\rightarrow\mathrm{t}=\frac{\pi}{\mathrm{2}}}\end{cases} \\ $$$$\mathrm{L}\:=\int_{\pi/\mathrm{2}} ^{\:\pi/\mathrm{4}}…
Question Number 64320 by aliesam last updated on 16/Jul/19 $${without}\:{beta}\:{function} \\ $$$$\int{cos}^{\mathrm{3}} {t}\:{sin}^{\mathrm{2}} {t}\:{dt}\: \\ $$ Commented by mathmax by abdo last updated on 16/Jul/19…
Question Number 129855 by liberty last updated on 20/Jan/21 $$\:\vartheta\:=\:\int\:\frac{{dx}}{\left(\mathrm{1}+\sqrt{{x}}\:\right)^{\mathrm{3}} } \\ $$ Answered by EDWIN88 last updated on 20/Jan/21 $$\vartheta\:=\:\int\:\frac{\mathrm{dx}}{\left(\sqrt{\mathrm{x}}\right)^{\mathrm{3}} \left(\mathrm{1}+\mathrm{x}^{−\mathrm{1}/\mathrm{2}} \right)^{\mathrm{3}} }=\:\int\:\frac{\mathrm{x}^{−\mathrm{3}/\mathrm{2}} }{\left(\mathrm{1}+\mathrm{x}^{−\mathrm{1}/\mathrm{2}}…
Question Number 64305 by aliesam last updated on 16/Jul/19 Commented by aliesam last updated on 16/Jul/19 $${prove}\:{that} \\ $$ Commented by mathmax by abdo last…
Question Number 129839 by liberty last updated on 20/Jan/21 Answered by EDWIN88 last updated on 20/Jan/21 $$\mathrm{J}=\int_{\:\mathrm{0}} ^{\:\pi/\mathrm{2}} \:\frac{\mathrm{3}\sqrt{\mathrm{cos}\:\mathrm{x}}}{\left(\sqrt{\mathrm{cos}\:\mathrm{x}}\:+\sqrt{\mathrm{sin}\:\mathrm{x}}\:\right)^{\mathrm{5}} }\:\mathrm{dx}\: \\ $$$$\:\mathrm{let}\:\mathrm{x}=\frac{\pi}{\mathrm{2}}−\mathrm{t}\:\Rightarrow\mathrm{J}=\int_{\frac{\pi}{\mathrm{2}}} ^{\:\mathrm{0}} \:\frac{\mathrm{3}\sqrt{\mathrm{sin}\:\mathrm{t}}}{\left(\sqrt{\mathrm{sin}\:\mathrm{t}}\:+\sqrt{\mathrm{cos}\:\mathrm{t}}\right)^{\mathrm{5}} }\left(−\mathrm{dt}\right)…
Question Number 64302 by mathmax by abdo last updated on 16/Jul/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 129816 by BHOOPENDRA last updated on 19/Jan/21 Answered by mathmax by abdo last updated on 19/Jan/21 $$\int\int\int_{\mathrm{C}_{\mathrm{f}} } \mathrm{z}\:\mathrm{e}^{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} } \mathrm{dxdydz}\:=_{\begin{cases}{\mathrm{x}=\mathrm{rcos}\theta}\\{\mathrm{y}=\mathrm{rsin}\theta}\end{cases}} \:\:\:\int_{\mathrm{2}}…
Question Number 64270 by aliesam last updated on 16/Jul/19 $$\int\frac{\mathrm{5}{sin}\left({x}\right)\:{cos}\left({x}\right)}{\:\sqrt[{\mathrm{3}}]{{cos}\left({x}\right)+\mathrm{1}}}\:{dx} \\ $$ Answered by Tanmay chaudhury last updated on 16/Jul/19 $${t}^{\mathrm{3}} =\mathrm{1}+{cosx}\:\:\mathrm{3}{t}^{\mathrm{2}} {dt}=−{sinxdx} \\ $$$$\int\frac{\mathrm{5}×\left({t}^{\mathrm{3}}…