Question Number 128633 by Lordose last updated on 09/Jan/21 $$\Omega\:=\:\int_{\mathrm{0}} ^{\:\frac{\mathrm{1}}{\mathrm{3}}} \mathrm{x}^{\mathrm{2n}} \mathrm{ln}\left(\mathrm{1}−\mathrm{x}\right)\mathrm{dx} \\ $$ Answered by mathmax by abdo last updated on 09/Jan/21 $$\mathrm{let}\:\mathrm{try}\:\mathrm{another}\:\mathrm{way}\:\:\mathrm{x}=\frac{\mathrm{t}}{\mathrm{3}}\:\Rightarrow…
Question Number 63089 by mathmax by abdo last updated on 28/Jun/19 $${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{dx}}{\mathrm{1}+\left({tanx}\right)^{\sqrt{\mathrm{2}}} }\:. \\ $$ Commented by edafe ovwie last updated on 29/Jun/19…
Question Number 63084 by mathmax by abdo last updated on 28/Jun/19 $${let}\:{f}\left({z}\right)\:=\frac{{cos}\left(\mathrm{3}{z}\right)}{{z}^{\mathrm{2}} } \\ $$$${calculate}\:{Res}\left({f},\mathrm{0}\right)\:. \\ $$ Commented by mathmax by abdo last updated on…
Question Number 128620 by Ahmed1hamouda last updated on 08/Jan/21 Answered by TheSupreme last updated on 09/Jan/21 $${u}={x}+{y} \\ $$$${v}={x}−{y} \\ $$$${x}=\frac{{u}+{v}}{\mathrm{2}} \\ $$$${y}=\frac{{u}−{v}}{\mathrm{2}} \\ $$$${J}=\begin{bmatrix}{\frac{\mathrm{1}}{\mathrm{2}}\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{2}}}\\{\frac{\mathrm{1}}{\mathrm{2}}\:−\frac{\mathrm{1}}{\mathrm{2}}}\end{bmatrix}…
Question Number 63079 by mathmax by abdo last updated on 28/Jun/19 $${let}\:{f}\left({z}\right)\:=\frac{{sin}\left(\mathrm{2}{z}\right)}{{z}^{{n}} }\:\:\:\:{with}\:{n}\:{integr}\:{natural}\: \\ $$$${calculate}\:{Res}\left({f},\mathrm{0}\right) \\ $$ Commented by mathmax by abdo last updated on…
Question Number 63080 by Enebeli Chinedu Vitalis last updated on 28/Jun/19 $$\:\int\frac{\sqrt{\frac{{sinx}}{{x}^{\mathrm{3}} }}}{{x}^{\mathrm{3}} }{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 128610 by john_santu last updated on 08/Jan/21 $$\int_{−\pi/\mathrm{4}} ^{\:\pi/\mathrm{4}} \frac{\mathrm{sec}\:\mathrm{x}}{\mathrm{e}^{\mathrm{x}} +\mathrm{1}}\:\mathrm{dx}\: \\ $$ Commented by liberty last updated on 09/Jan/21 $$\mathrm{I}=−\int_{−\pi/\mathrm{4}} ^{\:\pi/\mathrm{4}} \frac{\mathrm{sec}\:\left(−\mathrm{x}\right)}{\mathrm{e}^{−\mathrm{x}}…
Question Number 128608 by john_santu last updated on 08/Jan/21 $$\int\:\mathrm{x}^{\mathrm{2}} .\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{x}}{\mathrm{2}}\right)\mathrm{dx}=? \\ $$ Answered by liberty last updated on 08/Jan/21 $$\mathcal{L}\:=\:\frac{\mathrm{1}}{\mathrm{3}}\mathrm{x}^{\mathrm{3}} .\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{x}}{\mathrm{2}}\right)−\frac{\mathrm{1}}{\mathrm{3}}\int\frac{\mathrm{x}^{\mathrm{3}} \left(\frac{\mathrm{1}}{\mathrm{2}}\right)}{\mathrm{1}+\frac{\mathrm{x}^{\mathrm{2}}…
Question Number 128602 by Ahmed1hamouda last updated on 08/Jan/21 $$\int_{−\mathrm{1}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\mathrm{1}−{x}} \sqrt{\frac{{x}^{\frac{\mathrm{2}}{\mathrm{3}}} {y}−{x}^{\frac{\mathrm{5}}{\mathrm{3}}} {y}−{x}^{\frac{\mathrm{2}}{\mathrm{3}}} {y}^{\mathrm{2}} }{{y}^{\mathrm{2}} }}{dydx} \\ $$$$ \\ $$ Answered by…
Question Number 128570 by mnjuly1970 last updated on 08/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{mathematical}\:\:{analysis}… \\ $$$$\:\:{if}\:''\:\:{f}\:\:\:''\:\:{is}\:\mathscr{R}{eimann}\:{integrable} \\ $$$$\:\:\:{function}\:\:{on}\:\left[{a}\:,\:{b}\:\right]\:,\:{then}\:{prove}:: \\ $$$$\:\:\:\:\: \\ $$$$\:\:{lim}_{{t}\rightarrow\infty\:} \left\{\int_{{a}} ^{\:{b}} {f}\left({x}\right){cos}\left({tx}\right){dx}\:\right\}=\mathrm{0} \\ $$$$\:\:..\mathscr{R}{eimann}−\mathscr{L}{ebesgue}\:\:{theorem}… \\ $$$$…