Question Number 61534 by maxmathsup by imad last updated on 04/Jun/19 $${calculate}\:{f}\left({a}\right)\:=\int\int_{{W}} \:\left({x}+{ay}\right){e}^{−{x}} \:{e}^{−{ay}} {dxdy}\:{with} \\ $$$${W}_{{a}} =\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /{x}\geqslant\mathrm{0}\:,{y}\geqslant\mathrm{0}\:\:\:,\:{x}+{ay}\:\leqslant\mathrm{1}\:\right\}\:\:\:{a}>\mathrm{0} \\ $$ Terms of Service Privacy…
Question Number 61530 by maxmathsup by imad last updated on 04/Jun/19 $${let}\:{U}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{x}^{−\mathrm{2}{n}} }{\mathrm{1}+{x}^{\mathrm{4}} }\:{dx}\:\:\:{with}\:{n}\:{integr}\:{natural}\:{and}\:\:\:{n}\geqslant\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{U}_{{n}} \:{interms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{n}^{\mathrm{2}} \:{U}_{{n}} \\…
Question Number 61528 by maxmathsup by imad last updated on 04/Jun/19 $${find}\:\:\int_{\mathrm{0}} ^{\infty} \:\:{cos}\left({zx}^{\mathrm{2}} \right){dx}\:{with}\:{z}\:\in\:{C}\:. \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 61529 by maxmathsup by imad last updated on 04/Jun/19 $${find}\:\int_{\mathrm{0}} ^{\infty} \:\:{x}^{\mathrm{2}} {e}^{−{zx}^{\mathrm{2}} } {dx}\:\:{with}\:{z}\:{from}\:{C}\: \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 61522 by YSN 1905 last updated on 03/Jun/19 $${I}=\int\frac{\mathrm{sin}\:{x}.{e}^{\mathrm{cos}\:{x}} −\left(\mathrm{sin}\:{x}+\mathrm{cos}\:{x}\right){e}^{\left(\mathrm{sin}\:{x}+\mathrm{cos}\:{x}\right)} }{{e}^{\mathrm{2sin}\:{x}} −\mathrm{2}{e}^{\mathrm{sin}\:{x}} +\mathrm{1}}{dx} \\ $$ Answered by perlman last updated on 04/Jun/19 $${I}=\int\frac{{sin}\left({x}\right){e}^{{cos}\left({x}\right)}…
Question Number 127042 by benjo_mathlover last updated on 26/Dec/20 $$\:\int_{\mathrm{1}/\sqrt{\mathrm{2}}} ^{\:\mathrm{1}} \frac{\mathrm{arcsin}\:{x}}{{x}^{\mathrm{3}} }\:{dx}\:? \\ $$$$\:'\:{not}\:{nice}\:{integral}\:'\: \\ $$ Commented by liberty last updated on 26/Dec/20 ��������…
Question Number 127032 by mnjuly1970 last updated on 26/Dec/20 Answered by Olaf last updated on 26/Dec/20 $$\left.{i}\right) \\ $$$$\mathrm{1}−\mathrm{2}{r}\mathrm{cos}{x}+{r}^{\mathrm{2}} \:=\:\left({e}^{{ix}} −{r}\right)\left({e}^{−{ix}} −{r}\right) \\ $$$$\mathrm{R}_{{x}} \left({r}\right)\:=\:\frac{\mathrm{1}−{r}^{\mathrm{2}}…
Question Number 127020 by bramlexs22 last updated on 26/Dec/20 $$\:\:{super}\:{nice}\:! \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{show}\:{that}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\zeta\left(\mathrm{6}\right)\:=\:\frac{\pi^{\mathrm{6}} }{\mathrm{945}} \\ $$ Commented by liberty last updated on 26/Dec/20 $${hahaha}\:{very}\:{nice}\:…
Question Number 127017 by mnjuly1970 last updated on 26/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{NICE}\:\:\:\:\:{CALCULUS}… \\ $$$$\:\:{prove}\:{that}\::: \\ $$$$\int_{\mathrm{0}} ^{\:\infty} \:\left(\frac{{x}^{\mathrm{2}} {ln}\left(\pi{x}\right)}{\pi^{\pi{x}} }\right){dx} \\ $$$$\:\:=\frac{\mathrm{1}}{\left(\pi{ln}\left(\pi\right)\right)^{\mathrm{3}} }\left[\left(\mathrm{3}−\mathrm{2}\left(\gamma+{ln}\left({ln}\left(\pi\right)\right)\right)\right]\right. \\ $$ Answered by…
Question Number 192543 by peter frank last updated on 20/May/23 Answered by leodera last updated on 20/May/23 $$\Delta\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{sin}\:\left({x}\right)}{\mathrm{sin}\:\left({x}\right)+\mathrm{cos}\:\left({x}\right)}{dx} \\ $$$$\Delta\:=\:\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{sin}\:\left({x}\right)+\mathrm{cos}\:\left({x}\right)}{\mathrm{sin}\:\left({x}\right)+\mathrm{cos}\:\left({x}\right)}{dx}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}}…