Question Number 78708 by abdomathmax last updated on 20/Jan/20 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{e}^{−{x}} }{{x}}\left({sinx}\right)^{\mathrm{2}\:} {dx} \\ $$ Commented by mathmax by abdo last updated on 21/Jan/20…
Question Number 78706 by abdomathmax last updated on 20/Jan/20 $${calculate}\:\int\int_{\left[\mathrm{0},\mathrm{1}\right]^{\mathrm{2}} } \:\:\:\frac{{dxdy}}{\left({x}+{y}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$ Answered by mind is power last updated on 20/Jan/20 $$=\int_{\mathrm{0}}…
Question Number 78705 by abdomathmax last updated on 20/Jan/20 $${calculate}\:\int\int_{{D}} \:\left({x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \right){dxdy}\: \\ $$$${D}\:=\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /\:\frac{\mathrm{1}}{\mathrm{2}}\leqslant{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \leqslant\mathrm{3}\:{and}\:{y}\geqslant\mathrm{0}\right\} \\ $$ Answered by mind is power…
Question Number 78707 by abdomathmax last updated on 20/Jan/20 $${let}\:{I}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}+{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx}\:{and}\: \\ $$$${J}\:=\int\int_{\left[\mathrm{0},\mathrm{1}\right]^{\mathrm{2}} } \:\:\:\:\frac{{x}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{xy}\right)}{dxdy} \\ $$$${find}\:{J}\:{by}\:{two}\:{method}\:{and}\:{deduce}\:\:{the}\:{valueof}\:{I} \\ $$ Answered by mind…
Question Number 78703 by abdomathmax last updated on 20/Jan/20 $${let}\:{a}>\mathrm{0}\:\:{calculate}\:\int\int_{{D}_{{a}} } \:\:\:\:\frac{{xdxdy}}{{a}^{\mathrm{2}} \:+{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} } \\ $$$${and}\:{D}_{{a}} =\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /\:{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \leqslant{a}^{\mathrm{2}} \:\:{and}\:{x}>\mathrm{0}\right\} \\ $$ Answered…
Question Number 78700 by abdomathmax last updated on 20/Jan/20 $${calculate}\:\int\int_{{D}} \:\frac{\mid{x}−\mathrm{2}\mid}{{y}}{dxdy}\:{with} \\ $$$${D}=\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /\mathrm{0}\leqslant{x}\leqslant\mathrm{3}\:{and}\:\:\mathrm{1}\leqslant{y}\leqslant{e}\right\} \\ $$ Commented by john santu last updated on 20/Jan/20 $$=\:\int_{\mathrm{1}}…
Question Number 78701 by abdomathmax last updated on 20/Jan/20 $${calculate}\:\int\int_{{D}} \:\:\frac{{dxdy}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{y}^{\mathrm{2}} \right)} \\ $$$${with}\:{D}\:=\left\{\left({x},{h}\right)\in{R}^{\mathrm{2}} \:\:/\mathrm{0}\leqslant{x}\leqslant\mathrm{1}\:{and}\:\:\mathrm{0}\leqslant{y}\:\leqslant{x}\right\} \\ $$ Commented by john santu last updated on…
Question Number 144231 by mnjuly1970 last updated on 23/Jun/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…..{Nice}\:…{Calculus} \\ $$$$\:\:\:\:\:\:{if}\:\:::\:\: \\ $$$$\:\:\:\:\:\:\:\varphi\:\left(\:{n}\:\right)\::=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{x}^{\:{n}} }{\mathrm{1}\:+\:{x}}\:{dx} \\ $$$$\:\:\:\:\:{then}\:\:::\:\:\:\underset{{n}=\mathrm{1}} {\overset{\:\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} \:\varphi\:\left({n}\:\right)}{{n}}\:=? \\ $$$$\:\:\:\:\:\:\:…….. \\…
Question Number 78655 by Pratah last updated on 19/Jan/20 Commented by mr W last updated on 19/Jan/20 $$={e}^{{e}^{…^{{e}^{{e}} } } } −{e}^{{e}^{…^{{e}} } } \\…
Question Number 144187 by ArielVyny last updated on 22/Jun/21 $$\int_{\mathrm{0}} ^{+\infty} \frac{{u}^{\mathrm{2}} }{{u}^{\mathrm{8}} +\mathrm{2}{u}^{\mathrm{4}} +\mathrm{1}}{du} \\ $$ Answered by Ar Brandon last updated on 22/Jun/21…