Category: Integration

Question Number 30775 by abdo imad last updated on 25/Feb/18 $$let\alpha \in ]0,\pi [calculate{\int }_0^{\frac{\pi }{2}}\frac{dx}{2(cos\alpha +chx)}.$$ Commented by prof Abdo imad last updated on 25/Feb/18 $${we}\:{have}\:{I}\:=\:\int_{\mathrm{0}}…

Question Number 30773 by abdo imad last updated on 25/Feb/18 $$leta>0calculate{\int }_0^{\mathrm{\infty }}\frac{dx}{{(x^2+a^2)}^2}$$$$\left.\mathrm{2}\right)\:{calculate}\:\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{x}^{\mathrm{2}} }{\left({x}^{\mathrm{2}} \:+{a}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx}. \…

Question Number 30767 by abdo imad last updated on 25/Feb/18 $$calculate{A}_n={\int }_0^1\frac{1-\sqrt{x}}{1{-}^n\sqrt{x}}dx.$$ Commented by abdo imad last updated on 25/Feb/18…

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}}…