Question Number 170535 by mathlove last updated on 26/May/22 $$\int_{{c}} \left({cosxsiny}−{xy}\right){dx}+\left({sinx}\:\centerdot{cosy}\right){dy} \\ $$$${faind}\:{integral}\:{on}\:{the}\:{opposite} \\ $$$${sid}\:{of}\:{the}\:{clock}\:{face}\:{in}\:{the} \\ $$$${c}\:{unit}\:{circle}? \\ $$$${solve}\:{this} \\ $$ Commented by mathlove last…
Question Number 170532 by MikeH last updated on 26/May/22 $$\mathrm{Let}\:{I}_{{n}} \:=\int{x}^{{n}} {e}^{−{x}} {dx},\:{n}\:=\:\mathrm{0},\mathrm{1},\mathrm{2},… \\ $$$$\left(\mathrm{i}\right)\:\mathrm{Show}\:\mathrm{that}\:{I}_{{n}} \:=\:−{x}^{{n}} {e}^{−{x}} +{nI}_{{n}−\mathrm{1}} \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{Show}\:\mathrm{that}\:\int_{\mathrm{0}} ^{\infty} {x}^{{n}} {e}^{−{x}} {dx}\:=\:{n}! \\…
Question Number 104980 by I want to learn more last updated on 25/Jul/20 Commented by Dwaipayan Shikari last updated on 25/Jul/20 Commented by I want…
Question Number 170519 by nimnim last updated on 25/May/22 $$\:\:\:\:{Evaluate}\::\:\:\:\int_{−\mathrm{1}} ^{\:+\mathrm{1}} \frac{{x}^{\mathrm{2}} }{\mathrm{1}+\mathrm{2}^{{x}} }{dx} \\ $$$$\:\:\:\:{Please}\:{help}\:{me}.. \\ $$ Answered by Mathspace last updated on 26/May/22…
Question Number 39443 by rahul 19 last updated on 06/Jul/18 $$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\left[\:\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{2}} +\mathrm{1}}+\:\frac{\mathrm{2}}{\mathrm{n}^{\mathrm{2}} +\mathrm{2}}+\:\frac{\mathrm{3}}{\mathrm{n}^{\mathrm{2}} +\mathrm{3}}+\:….+\frac{\mathrm{1}}{\mathrm{n}+\mathrm{1}}\right]\:=\:? \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 06/Jul/18 $${very}\:{good}…{this}\:{is}\:{the}\:{way}\:{to}\:{solve}\:{it}……
Question Number 39440 by rahul 19 last updated on 06/Jul/18 $$\mathrm{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{\:{x}_{} } \:{e}^{{t}\:} \left(\frac{\mathrm{1}+\mathrm{sin}\:{t}}{\mathrm{1}+\mathrm{cos}\:{t}}\right)\:{dt}. \\ $$$${T}\mathrm{hen}\:\:\mathrm{f}\left(\frac{\pi}{\mathrm{3}}\right)×\mathrm{f}\left(\frac{\mathrm{2}\pi}{\mathrm{3}}\right)\:=\:? \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on…
Question Number 39441 by rahul 19 last updated on 06/Jul/18 $$\int_{\frac{\mathrm{1}}{\mathrm{4}}} ^{\:\mathrm{4}} \:\frac{\mathrm{1}}{{x}}\:\mathrm{sin}\:\left({x}−\frac{\mathrm{1}}{{x}}\right){dx}\:=\:? \\ $$ Commented by prof Abdo imad last updated on 06/Jul/18 $${changement}\:\:{x}=\frac{\mathrm{1}}{{t}}\:\:{give}…
Question Number 170501 by kndramaths last updated on 25/May/22 $$\:\:\:\:\:\:\:\:\:\:{solve}\:{this}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\int_{{D}} {x}^{\mathrm{2}} {e}^{{xy}} {dxdy} \\ $$$${D}:\left\{\left({x}.{y}\right)\in{R}^{\mathrm{2}} \:/\mathrm{0}\leqslant{x}\leqslant\mathrm{1}.\:\:\mathrm{0}\leqslant{y}\leqslant\mathrm{2}\right\} \\ $$$$\:\:\:\:\:\:\int\underset{{D}} {\int}\frac{{ydxdy}}{\left(\mathrm{1}+{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)^{\frac{\mathrm{3}}{\mathrm{2}}} }.\:\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1}.\mathrm{0}\leqslant{y}\leqslant\mathrm{1}. \\…
Question Number 39431 by rahul 19 last updated on 06/Jul/18 $$\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\mathrm{e}^{\frac{{x}}{\mathrm{2}}} \mathrm{sin}\:\left(\frac{{x}}{\mathrm{2}}+\frac{\pi}{\mathrm{4}}\right)\mathrm{d}{x}\:=\:? \\ $$ Commented by prof Abdo imad last updated on 06/Jul/18…
Question Number 170475 by mnjuly1970 last updated on 24/May/22 $$ \\ $$$$\:\:\:\:\:\:\:{An}\:{easy}\:{question}\:{of}\:{Measure}\:{theory}: \\ $$$$ \\ $$$$\:\:\:\:\:{Prove}\:{that}\::\:\:\:\:\:\:\:\:\:\:\:\:\:\mu\:\left(\:\mathrm{Q}\:\right)=\mathrm{0}\:\:\:\:\:\:\:\:\:\:\:\:\:\blacksquare{m}.{n} \\ $$$$ \\ $$ Terms of Service Privacy Policy…