Category: Integration

Question Number 37278 by abdo.msup.com last updated on 11/Jun/18 $$\:{calculate}\:\int\int_{{D}} \:{x}\:{cos}\left({x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \right){dxdy} \\ $$$${with}\:{D}=\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1}\:{and}\right. \\ $$$$\left.\mathrm{1}\leqslant{y}\leqslant\mathrm{3}\right\} \\ $$ Commented by prof Abdo imad…

Question Number 37275 by abdo.msup.com last updated on 11/Jun/18 $${let}\:{A}_{{n}} \:=\:\int_{\mathrm{0}} ^{\frac{\mathrm{1}}{{n}}} \:{arctan}\left(\mathrm{1}+{x}^{\mathrm{2}} \right){dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right){find}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \:. \\ $$ Terms of Service…

Question Number 168341 by Tibo last updated on 08/Apr/22 $$\int\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{3}} {dx}=? \\ $$ Answered by Florian last updated on 08/Apr/22 $$\:\:=\:\int\mathrm{1}+\mathrm{3}{x}^{\mathrm{2}} +\mathrm{3}{x}^{\mathrm{4}} +{x}^{\mathrm{6}} {dx}…

Question Number 37270 by abdo.msup.com last updated on 11/Jun/18 $${find}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \left(\frac{\mathrm{1}−{x}^{{n}+\mathrm{1}} }{\mathrm{1}−{x}}\right)^{\mathrm{2}} {dx}\:. \\ $$ Answered by abdo.msup.com last updated on 27/Jul/18 $${let}\:{I}\:=\:\int_{\mathrm{0}} ^{\mathrm{1}}…

Question Number 168338 by infinityaction last updated on 08/Apr/22 Answered by Mathspace last updated on 08/Apr/22 $$\int_{\mathrm{0}} ^{\infty} \:\:\frac{{sin}^{\mathrm{2}} \left({ax}\right)}{{x}^{\mathrm{2}} }{dx}\:\:\:\:{a}>\mathrm{0} \\ $$$$=_{{ax}={t}} \:\:\int_{\mathrm{0}} ^{\infty}…