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Question Number 159552 by Ar Brandon last updated on 18/Nov/21 Commented by Ar Brandon last updated on 18/Nov/21 $$\mathrm{Prove}\:\mathrm{the}\:\mathrm{above}\:\mathrm{results} \\ $$ Commented by mindispower last…
Question Number 28448 by abdo imad last updated on 25/Jan/18 $${find}\:\int\int_{{D}} \:\:\:\:\frac{{xy}}{\mathrm{1}+{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }{dxdy}\:{with} \\ $$$${D}=\:\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /\:\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \geqslant\mathrm{1}\:\:\right\}\:\:. \\ $$ Answered by ajfour last…
Question Number 28444 by abdo imad last updated on 25/Jan/18 $${let}\:{give}\:\:\mathrm{1}<{a}<{b}\:\:{and}\:{I}=\:\int_{\mathrm{0}} ^{\pi} \:\int_{{a}} ^{{b}} \:\:\frac{{du}}{{x}−{cosu}}\:{dt}\:\:{find}\:{the} \\ $$$${value}\:{of}\:\int_{\mathrm{0}} ^{\pi} \:\:{ln}\left(\frac{{b}−{cost}}{{a}−{cost}}\right){dt}\:. \\ $$ Terms of Service Privacy…
Question Number 28445 by abdo imad last updated on 25/Jan/18 $${find}\:\int\int_{{x}\leqslant{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \:\leqslant\mathrm{1}} \:\:\frac{{dxdy}}{\left(\mathrm{1}+{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)}\:\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 28446 by abdo imad last updated on 25/Jan/18 $${find}\:\int\int_{{A}} \left({x}+{y}\right)\:{e}^{−{x}} \:{e}^{−{y}} \:{dxdy}\:{with} \\ $$$${A}=\:\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} \:\:/{x}\geqslant\mathrm{0}\:,{y}\geqslant\mathrm{0}\:,\:{x}+{y}\:\leqslant\mathrm{1}\:\right\}\:\:. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 28442 by abdo imad last updated on 25/Jan/18 $${let}\:{give}\:{B}\left({x},{y}\right)=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{u}^{{x}−\mathrm{1}} \left(\mathrm{1}−{u}\right)^{{y}−\mathrm{1}} {du}\:\:{and}\:\left({beta}\:{function}\right) \\ $$$${and}\:\Gamma\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:{u}^{{x}−\mathrm{1}} \:{e}^{−{u}} \:{du}\:\:\:\:\:\left({x}>\mathrm{0}\right)\left({gamma}\:{function}\:{of}\:{euler}\right) \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:\:\:\:\Gamma\left({x}\right)=\:\mathrm{2}\int_{\mathrm{0}} ^{\infty} \:{u}^{\mathrm{2}{x}−\mathrm{1}}…
Question Number 28438 by abdo imad last updated on 25/Jan/18 $${find}\:\:{I}=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dt}}{\left(\mathrm{1}+{t}^{\mathrm{4}} \right)^{{n}} }\:\:{with}\:{n}\:{integr}\:{and}\:{n}\neq\mathrm{0}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 28439 by abdo imad last updated on 25/Jan/18 $${find}\:\:\int\:\:\frac{\mathrm{1}+{tanx}}{\mathrm{1}+{sin}^{\mathrm{2}} {x}}{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 28427 by abdo imad last updated on 25/Jan/18 $${find}\:\int\int_{{D}} \sqrt{\mathrm{2}−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} }\:\:{dxdy}\:\:{with} \\ $$$${D}=\:\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /\:\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \:\leqslant\sqrt{\mathrm{2}}\:\right\} \\ $$ Commented by abdo imad…