Category: Integration

Question Number 161839 by mathmax by abdo last updated on 23/Dec/21 $$\mathrm{calculate}{\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}\frac{\mathrm{dx}}{{({\mathrm{x}}^2+2\mathrm{x}+2)}^2}$$ Answered by ArielVyny last updated on 23/Dec/21…

Question Number 30764 by abdo imad last updated on 25/Feb/18 $$let{I}_n={\int }_0^{\frac{1}{2}}{(1-2t)}^n{e}^{-t}dtwithnintegrnot0$$$$1)provethat\mathrm{\forall }t\in [0,\frac{1}{2}]$$$$\frac{\mathrm{1}}{\:\sqrt{{e}}}\left(\mathrm{1}−\mathrm{2}{t}\right)^{{n}} \leqslant\:\left(\mathrm{1}−\mathrm{2}{t}\right)^{{n}} \:{e}^{−{t}} \:\leqslant\left(\mathrm{1}−\mathrm{2}{t}\right)^{{n}} \:{then}\:{find}\:{lim}_{{n}\rightarrow\infty\:} {I}_{{n}}…

Question Number 30761 by abdo imad last updated on 25/Feb/18 $$find{\int }_0^{\mathrm{\infty }}{x}^{2n+1}{e}^{-x^2}dxwithnfromN.$$ Commented by abdo imad last updated on…

Question Number 161830 by EnterUsername last updated on 22/Dec/21 $$\int \frac{dx}{\sqrt{1-x^{14}}}$$ Answered by Ar Brandon last updated on 22/Dec/21 $$\mathrm{arcsin}\left({x}\right)=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{{x}^{\mathrm{2}{n}+\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{2}}\right)_{{n}}…

Question Number 30741 by abdo imad last updated on 25/Feb/18 $$letgiveD=R_{+}^2-\left\{(0,0)\right\}and\alpha fromRlet$$$$C_1=\{(x,y)\in D/0<x^2+y^2⩽1\}$$$$C_2=\{(x,y)\in D/x^2+y^2⩾1\}studytheconvergenceof$$$${I}=\:\int\int_{{C}_{\mathrm{1}}…