Question Number 108429 by Rasikh last updated on 16/Aug/20 Answered by Sarah85 last updated on 17/Aug/20 $$\int\mathrm{e}^{{x}^{\mathrm{2}} } {dx}=\frac{\sqrt{\pi}}{\mathrm{2}}\int\frac{\mathrm{2e}^{{x}^{\mathrm{2}} } }{\:\sqrt{\pi}}{dx}=\frac{\sqrt{\pi}}{\mathrm{2}}\mathrm{erfi}\:\left({x}\right)\:+{C} \\ $$ Commented by…
Question Number 42870 by maxmathsup by imad last updated on 03/Sep/18 $${let}\:\mathrm{0}<{x}<\mathrm{1}\:\:{and}\:\Gamma\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:{t}^{{x}−\mathrm{1}} \:{e}^{−{t}} \:{dt}\: \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:\Gamma\left({x}\right).\Gamma\left(\mathrm{1}−{x}\right)\:=\frac{\pi}{{sin}\left(\pi{x}\right)}\:\:\:\left({compliments}\:{formulae}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\Gamma\left({n}\right)\:{and}\:\Gamma\left({n}+\frac{\mathrm{1}}{\mathrm{2}}\right)\:{with}\:{n}\:{from}\:{N}. \\ $$ Terms of Service…
Question Number 108401 by bobhans last updated on 16/Aug/20 $$\:\:\:\frac{\boldsymbol{{bobhans}}}{\ddots\iddots} \\ $$$$\:{I}=\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\mathrm{ln}\:\left({a}^{\mathrm{2}} \mathrm{cos}^{\mathrm{2}} \:\theta\:+\:{b}^{\mathrm{2}} \:\mathrm{sin}^{\mathrm{2}} \:\theta\:\right)\:{d}\theta\:?\: \\ $$ Commented by john santu last…
Question Number 108391 by bemath last updated on 16/Aug/20 $$\:\:\:\frac{\measuredangle\:\mathcal{B}{e}\mathcal{M}{ath}\:\measuredangle}{\bigtriangledown} \\ $$$${I}\:=\:\underset{\mathrm{0}} {\overset{\pi} {\int}}\:\frac{{x}\:{dx}}{\mathrm{1}+\mathrm{sin}\:{x}} \\ $$ Answered by bobhans last updated on 16/Aug/20 Commented by…
Question Number 108384 by bobhans last updated on 16/Aug/20 $$\left(\mathrm{1}\right)\int\:\frac{\sqrt{\mathrm{sin}\:{x}}}{\:\sqrt{\mathrm{sin}\:{x}}\:+\:\sqrt{\mathrm{cos}\:{x}}}\:{dx}\:? \\ $$$$\left(\mathrm{2}\right)\:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }−\mathrm{2}\frac{{dy}}{{dx}}\:+{y}\:=\:{e}^{{x}} \\ $$ Answered by bemath last updated on 16/Aug/20 Commented by…
Question Number 108382 by bobhans last updated on 16/Aug/20 $$\:\:\:\frac{\boldsymbol{{bobhans}}}{\iddots\ddots} \\ $$$$\:\underset{\pi/\mathrm{2}} {\overset{\pi} {\int}}\mid\:\mathrm{cos}\:{x}−\mathrm{sin}\:{x}\:\mid\:{dx}\:? \\ $$$$ \\ $$ Commented by PRITHWISH SEN 2 last updated…
Question Number 173908 by ali009 last updated on 20/Jul/22 $${find}\:{the}\:{value}\:{of}\:{b}\:{so}\:{that}\:{the}\:{line}\:{y}={b} \\ $$$${divides}\:{the}\:{region}\:{bound}\:{by}\:{the}\:{graphs}\:{of} \\ $$$${the}\:{two}\:{functinos}\:,\:{into}\:{two}\:{regions}\:{of}\:{equal} \\ $$$${area}. \\ $$$${f}\left({x}\right)=\mathrm{9}−{x}^{\mathrm{2}} \:{and}\:{g}\left({x}\right)=\mathrm{0} \\ $$ Commented by mr W…
Question Number 42823 by rahul 19 last updated on 03/Sep/18 $$\mathrm{Evaluate}\:: \\ $$$$\int_{−\mathrm{5}} ^{\:\mathrm{5}} \:{x}^{\mathrm{2}} \left[{x}+\frac{\mathrm{1}}{\mathrm{2}}\right]{dx}\:=\:\:? \\ $$$${where}\:\left[.\right]=\:{greatest}\:{integer}\:{function} \\ $$ Commented by prof Abdo imad…
Question Number 42812 by maxmathsup by imad last updated on 02/Sep/18 $${study}\:{the}\:{convervence}\:{of}\:\:\int_{\mathrm{1}} ^{+\infty} \:\:\frac{{arctan}\left({x}−\mathrm{1}\right)}{\left({x}^{\mathrm{2}} −\mathrm{1}\right)^{\frac{\mathrm{4}}{\mathrm{3}}} }\:{dx} \\ $$ Commented by maxmathsup by imad last updated…
Question Number 42810 by maxmathsup by imad last updated on 02/Sep/18 $${find}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{x}^{\mathrm{5}} }{\mathrm{1}+{x}^{\mathrm{7}} }{dx}\:\:. \\ $$ Commented by prof Abdo imad last updated…