Question Number 159233 by mnjuly1970 last updated on 14/Nov/21 Answered by mindispower last updated on 16/Nov/21 $${A}_{\mathrm{2}{n}} =\underset{{k}\geqslant\mathrm{1}} {\sum}\frac{\mathrm{1}}{\left(\mathrm{2}{k}\right)^{\mathrm{2}{n}} }=\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}{n}} }.\zeta\left(\mathrm{2}{n}\right) \\ $$$$\frac{\frac{\zeta\left(\mathrm{2}{n}\right)}{\mathrm{2}^{\mathrm{2}{n}} }}{\mathrm{2}{n}\left(\mathrm{2}{n}+\mathrm{1}\right)}=−\frac{\zeta\left(\mathrm{2}{n}\right)}{\mathrm{2}^{\mathrm{2}{n}} \left(\mathrm{2}{n}+\mathrm{1}\right)}+\frac{\zeta\left(\mathrm{2}{n}\right)}{\mathrm{2}^{\mathrm{2}{n}}…
Question Number 28162 by abdo imad last updated on 21/Jan/18 $${find}\:\:\int_{\frac{\mathrm{1}}{\mathrm{2}}} ^{\mathrm{2}} \left(\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right){arctanxdx}. \\ $$ Commented by abdo imad last updated on 23/Jan/18 $${by}\:{parts}\:{u}^{,}…
Question Number 28160 by abdo imad last updated on 21/Jan/18 $${find}\:\int\int_{{D}} \:\:\sqrt{{xy}}\:{dxdy}\:{with}\:{D}=\left\{\left({x},{y}\right)\in{R}^{} \:/\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)^{\mathrm{2}} \leqslant{xy}\right\} \\ $$ Commented by abdo imad last updated on…
Question Number 28161 by abdo imad last updated on 21/Jan/18 $${find}\:{the}\:{value}\:{of}\:\int\int_{{W}} {ln}\left(\mathrm{1}+{x}+{y}\right){dxdy}\:{with} \\ $$$${W}=\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /\:{x}+{y}\leqslant\mathrm{1}\:{and}\:{x}\geqslant\mathrm{0}\:{and}\:{y}\geqslant\mathrm{0}\right\}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 28159 by abdo imad last updated on 21/Jan/18 $${let}\:{give}\:{D}=\left[\mathrm{0},\frac{\pi}{\mathrm{2}}\right]×\left[\mathrm{0},\frac{\mathrm{1}}{\mathrm{2}}\right]\:\:{find}\:{the}\:{value}\:{of} \\ $$$$\int\int_{{D}} \:\:\:\frac{{dxdy}}{{ycosx}\:+\mathrm{1}}\:\:. \\ $$ Commented by abdo imad last updated on 26/Jan/18 $${let}\:{put}\:\:{I}=\int\int_{{D}}…
Question Number 28158 by abdo imad last updated on 21/Jan/18 $${calculate}\:\int\int_{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \leqslant\mathrm{1}} \:\:\:\frac{{dxdy}}{\mathrm{3}+{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }\:\:. \\ $$ Answered by ajfour last updated on 21/Jan/18…
Question Number 159226 by cortano last updated on 14/Nov/21 $$\:\Omega\:=\:\int_{\mathrm{0}} ^{\infty} \frac{\sqrt[{\mathrm{6}}]{{x}^{\mathrm{5}} }−\sqrt{{x}}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\:\mathrm{ln}\:{x}}\:{dx}\:=? \\ $$ Answered by mindispower last updated on 14/Nov/21 $$\int_{\mathrm{0}} ^{\infty}…
Question Number 93683 by i jagooll last updated on 14/May/20 $$\int\:\left(\mathrm{t}^{\mathrm{2}} \boldsymbol{\mathrm{i}}\:+\mathrm{cos}\:\mathrm{2t}\boldsymbol{\mathrm{j}}\:+\mathrm{e}^{−\mathrm{t}} \boldsymbol{\mathrm{k}}\right)\:\mathrm{dt}\: \\ $$ Answered by john santu last updated on 14/May/20 $$=\:\frac{\mathrm{1}}{\mathrm{3}}\mathrm{t}^{\mathrm{3}} \:\overset{\rightarrow}…
Question Number 93638 by i jagooll last updated on 14/May/20 $$\int\:\frac{{x}^{\mathrm{4}} +\mathrm{4}{x}^{\mathrm{2}} }{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{4}}}\:{dx}\:?\: \\ $$ Commented by i jagooll last updated on 14/May/20 $$\mathrm{thank}\:\mathrm{you}\:\mathrm{both}\:…
Question Number 93636 by abdomathmax last updated on 14/May/20 $${calcilate}\:{U}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\frac{{sin}\left({nx}\right)}{{e}^{{x}} −\mathrm{1}}{dx} \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com