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…
Question Number 104928 by bobhans last updated on 24/Jul/20 $$\int\:\left({e}^{{x}} −\left(\mathrm{2}{x}+\mathrm{3}\right)^{\mathrm{4}} \right)^{\mathrm{3}} \:{dx} \\ $$ Commented by kaivan.ahmadi last updated on 24/Jul/20 $$\int\left({e}^{\mathrm{3}{x}} −\mathrm{3}{e}^{\mathrm{2}{x}} \left(\mathrm{2}{x}+\mathrm{3}\right)^{\mathrm{4}}…
Question Number 39389 by maxmathsup by imad last updated on 05/Jul/18 $${calculate}\:{F}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\:\frac{{dt}}{\mathrm{1}+\left(\mathrm{1}+{x}\left(\mathrm{1}+{t}^{\mathrm{2}} \right)\right)^{\mathrm{2}} } \\ $$ Commented by prof Abdo imad last updated…
Question Number 39386 by maxmathsup by imad last updated on 05/Jul/18 $${find}\:{the}\:{value}\:{of}\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\frac{{ln}\left(\mathrm{1}+{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$ Commented by abdo mathsup 649 cc last updated…
Question Number 39384 by rahul 19 last updated on 05/Jul/18 $$\mathrm{The}\:\mathrm{values}\:\mathrm{of}\:\mathrm{a}\:\mathrm{for}\:\mathrm{which}\:\mathrm{y}=\:\mathrm{a}{x}^{\mathrm{2}} +{ax}+\frac{\mathrm{1}}{\mathrm{24}} \\ $$$${and}\:{x}\:=\:{ay}^{\mathrm{2}} +{ay}+\frac{\mathrm{1}}{\mathrm{24}}\:{touch}\:{each}\:{other} \\ $$$${are} \\ $$$$\left.\mathrm{1}\left.\right)\:\frac{\mathrm{2}}{\mathrm{3}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}\right)\:\frac{\mathrm{3}}{\mathrm{2}} \\ $$$$\left.\mathrm{3}\left.\right)\:\frac{\mathrm{13}+\sqrt{\mathrm{601}}}{\mathrm{12}}\:\:\:\:\:\:\:\mathrm{4}\right)\:\frac{\mathrm{13}−\sqrt{\mathrm{601}}}{\mathrm{12}}. \\ $$ Answered by…
Question Number 39383 by maxmathsup by imad last updated on 05/Jul/18 $${calculate}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{3}}} \:\:\:\:\:\:\frac{{sinxdx}}{{cosx}\left(\mathrm{2}+{ln}\left({cosx}\right)\right.}\:. \\ $$ Commented by math khazana by abdo last updated on…
Question Number 39381 by rahul 19 last updated on 05/Jul/18 Answered by ajfour last updated on 06/Jul/18 $${f}\:'\left({x}\right)\geqslant\left[{f}\left({x}\right)\right]^{\mathrm{3}} +\left[{f}\left({x}\right)\right]^{−\mathrm{1}} \\ $$$${and}\:{f}\left(\mathrm{0}\right)=\mathrm{1}\:,\:\:{f}\left({a}\right)=\mathrm{3}^{\mathrm{1}/\mathrm{4}} \\ $$$$\Rightarrow\:\:\:\int_{\mathrm{1}} ^{\:\:{y}} \frac{{dy}}{{y}^{\mathrm{3}}…