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…
Question Number 34674 by math khazana by abdo last updated on 09/May/18 $${find}\:\:\:\int_{\mathrm{0}} ^{\pi} \:\:\:\frac{{x}\:{sinx}}{\mathrm{1}+{cos}^{\mathrm{2}} {x}}\:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 100207 by Rio Michael last updated on 25/Jun/20 $$\mathrm{Given}\:\mathrm{an}\:\mathrm{even}\:\mathrm{fuction}\:{f}\left({x}\right)\:\mathrm{such}\:\mathrm{that}\:\overset{{a}} {\int}_{−{a}} \:{f}\left({x}\right){dx}\:=\:\sqrt{{a}}\:\forall{a}\:\geqslant\mathrm{0} \\ $$$$\mathrm{find}\:\int_{\mathrm{3}} ^{\mathrm{4}} {f}\left({x}\right)\:{dx} \\ $$$$ \\ $$ Commented by mr W…
Question Number 165741 by metamorfose last updated on 07/Feb/22 $$\left.\int_{\mathrm{0}} ^{\pi} \frac{{dt}}{\mathrm{1}−{sina}.{cost}}=???\:,\:{a}\in\right]\mathrm{0},\frac{\pi}{\mathrm{2}}\left[\right. \\ $$ Answered by MJS_new last updated on 08/Feb/22 $$\left.{a}\in\right]\mathrm{0};\:\frac{\pi}{\mathrm{2}}\left[\:\Rightarrow\:\mathrm{0}<\mathrm{sin}\:{a}\:<\mathrm{1}\:\Rightarrow\:\mathrm{let}\:\mathrm{sin}\:{a}\:={A};\:\mathrm{0}<{A}<\mathrm{1}\right. \\ $$$$\int\frac{{dt}}{\mathrm{1}−{A}\mathrm{cos}\:{t}}= \\…
Question Number 165742 by amin96 last updated on 07/Feb/22 $$\boldsymbol{{prove}}\:\boldsymbol{{that}} \\ $$$$\underset{\boldsymbol{\mathrm{n}}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(\mathrm{2}\boldsymbol{\mathrm{n}}\right)!}{\left(\boldsymbol{\mathrm{n}}!\right)^{\mathrm{2}} \mathrm{4}^{\boldsymbol{\mathrm{n}}} \left(\mathrm{2}\boldsymbol{\mathrm{n}}+\mathrm{1}\right)^{\mathrm{4}} }\overset{?} {=}\frac{\pi}{\mathrm{96}}\left(\mathrm{12}\boldsymbol{\zeta}\left(\mathrm{3}\right)+\mathrm{8}\boldsymbol{\mathrm{ln}}^{\mathrm{3}} \left(\mathrm{2}\right)+\mathrm{2}\pi^{\mathrm{2}} \boldsymbol{\mathrm{ln}}\left(\mathrm{2}\right)\right) \\ $$$$ \\ $$$$−−−−−−−−\boldsymbol{{by}}\:\boldsymbol{{M}}.\boldsymbol{{A}} \\…