Question Number 144323 by qaz last updated on 24/Jun/21 $$\underset{\mathrm{i}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\left(−\mathrm{1}\right)^{\mathrm{n}+\mathrm{1}} }{\mathrm{n}}=? \\ $$ Answered by mathmax by abdo last updated on 25/Jun/21 $$\mathrm{A}_{\mathrm{n}}…
Question Number 144322 by qaz last updated on 24/Jun/21 $$\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(\mathrm{2n}\right)!!}{\left(\mathrm{2n}+\mathrm{1}\right)!!\left(\mathrm{n}+\mathrm{1}\right)}\mathrm{x}^{\mathrm{2n}+\mathrm{2}} =?……….\mid\mathrm{x}\mid\leqslant\mathrm{1} \\ $$ Answered by mindispower last updated on 25/Jun/21 $$\left(\mathrm{2}{n}\right)!!=\mathrm{2}^{{n}} .{n}! \\…
Question Number 78766 by M±th+et£s last updated on 20/Jan/20 $$\int\mathrm{2}\:{e}^{\frac{\mathrm{1}}{\mathrm{2}\left({x}−\mathrm{2}\right)^{\mathrm{2}} }} \:{dx} \\ $$ Answered by MJS last updated on 20/Jan/20 $$\mathrm{2}\int\mathrm{e}^{\frac{\mathrm{1}}{\mathrm{2}\left({x}−\mathrm{2}\right)^{\mathrm{2}} }} {dx}= \\…
Question Number 144248 by Pagnol last updated on 23/Jun/21 Answered by Ar Brandon last updated on 23/Jun/21 $$\mathrm{I}=\int\mathrm{tan}^{\mathrm{7}} \mathrm{xdx}=\int\mathrm{tan}^{\mathrm{5}} \mathrm{x}\left(\mathrm{sec}^{\mathrm{2}} \mathrm{x}−\mathrm{1}\right)\mathrm{dx} \\ $$$$\:\:=\frac{\mathrm{tan}^{\mathrm{6}} \mathrm{x}}{\mathrm{6}}−\int\mathrm{tan}^{\mathrm{3}} \mathrm{x}\left(\mathrm{sec}^{\mathrm{2}}…
Question Number 78717 by jagoll last updated on 20/Jan/20 $$\mathrm{given}\: \\ $$$$\int\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{dx}\:=\:\frac{\mathrm{1}}{\mathrm{2}\:\sqrt[{\mathrm{3}\:}]{\mathrm{g}\left(\mathrm{x}\right)}}\:.\: \\ $$$$\mathrm{g}'\left(\mathrm{1}\right)=\:\mathrm{g}\left(\mathrm{1}\right)\:=\:\mathrm{8}\:\Rightarrow\mathrm{f}\left(\mathrm{1}\right)=? \\ $$$$ \\ $$ Commented by john santu last updated on…
Question Number 144245 by ArielVyny last updated on 23/Jun/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{\mathrm{2}{n}} }{\left({x}−\mathrm{1}\right)^{{n}} }{dx} \\ $$ Answered by mathmax by abdo last updated on 23/Jun/21…
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…