Question Number 34715 by abdo mathsup 649 cc last updated on 10/May/18 $${calculate}\:\int\int_{\mathrm{0}\leqslant{x}\leqslant{y}\leqslant\mathrm{1}} \:\:\:\frac{{dxdy}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({y}^{\mathrm{2}} \:+\mathrm{3}\right)}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 34716 by abdo mathsup 649 cc last updated on 10/May/18 $${calculate}\:\int\int_{{w}} {x}\sqrt{{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} }\:\:{dxdy} \\ $$$${w}\:=\left\{\left({x},{y}\right)/\:{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:\leqslant\mathrm{3}\:\right\}\: \\ $$ Commented by prof…
Question Number 34717 by abdo mathsup 649 cc last updated on 10/May/18 $${let}\:{I}_{{n}} =\:\int\int_{\left[\frac{\mathrm{1}}{{n}},{n}\right]^{\mathrm{2}} } \:\:\:\:\:\frac{\sqrt{{xy}}\:{dxdy}}{\mathrm{2}\:+{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} } \\ $$$${find}\:{lim}\:{I}_{{n}} \:{when}\:{n}\rightarrow+\infty. \\ $$ Commented by…
Question Number 165787 by daus last updated on 08/Feb/22 $${find}\:\:\int{cos}^{\mathrm{3}} {x}\:{dx}\:? \\ $$ Answered by aleks041103 last updated on 08/Feb/22 $${cos}^{\mathrm{3}} {x}\:=\:{cosx}\left(\mathrm{1}−{sin}^{\mathrm{2}} {x}\right)= \\ $$$$={cosx}−{cosxsin}^{\mathrm{2}}…
Question Number 34714 by abdo mathsup 649 cc last updated on 10/May/18 $${calculate}\:\int\int_{{x}^{\mathrm{2}} \:+\mathrm{2}{y}^{\mathrm{2}} \:\leqslant\mathrm{1}} \left({x}^{\mathrm{2}} \:−{y}^{\mathrm{2}} \right){dxdy} \\ $$ Commented by math khazana by…
Question Number 34713 by abdo mathsup 649 cc last updated on 10/May/18 $${let}\:{a}>\mathrm{0}\:\:{calculate}\:\int\int_{{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:\leqslant\mathrm{3}} \:\frac{\mathrm{1}}{\mathrm{2}\:+{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} }{dxdy}. \\ $$ Commented by math khazana by…
Question Number 165757 by Zaynal last updated on 07/Feb/22 Answered by Mathspace last updated on 08/Feb/22 $${p}\left({x}\right)=\prod_{{n}=\mathrm{1}} ^{\mathrm{100}} \left({x}+{n}\right)\:\Rightarrow\frac{{p}^{'} \left({x}\right)}{{p}\left({x}\right)} \\ $$$$=\sum_{{n}=\mathrm{1}} ^{\mathrm{100}} \frac{\mathrm{1}}{{x}+{n}}\:\Rightarrow \\…
Question Number 100216 by Rio Michael last updated on 25/Jun/20 $$\mathrm{if}\:{I}\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{sin}\:{x}}{\mathrm{sin}\:{x}\:+\:\mathrm{cos}\:{x}}{dx}\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{cos}\:{x}}{\mathrm{sin}\:{x}\:+\mathrm{cos}\:{x}}{dx}\: \\ $$$$\mathrm{then}\:{I}\:=\:?? \\ $$ Commented by Dwaipayan Shikari last updated…
Question Number 100215 by Rio Michael last updated on 25/Jun/20 $$\mathrm{evaluate}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\int_{\mathrm{1}} ^{{e}} {x}^{{n}} \mathrm{ln}\:{x}\:{dx}\: \\ $$ Commented by Dwaipayan Shikari last updated on 25/Jun/20…
Question Number 34675 by math khazana by abdo last updated on 09/May/18 $${provethat}\:{e}\:=\:\sum_{{k}=\mathrm{0}} ^{{n}} \:\frac{\mathrm{1}}{{k}!}\:\:+\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{\left(\mathrm{1}−{t}\right)^{{n}} }{{n}!}\:{e}^{{t}} \:{dt}\:. \\ $$ Terms of Service Privacy…