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Category: Integration

calculate-f-cos-2x-1-ax-2-dx-with-a-gt-0-2-find-the-value-of-cos-2x-1-3x-2-dx-

Question Number 37288 by math khazana by abdo last updated on 11/Jun/18 $${calculate}\:\:{f}\left(\alpha\right)\:=\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{cos}\left(\mathrm{2}{x}\right)}{\mathrm{1}+{ax}^{\mathrm{2}} }\:{dx}\:{with}\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{−\infty} ^{+\infty} \:\:\:\:\frac{{cos}\left(\mathrm{2}{x}\right)}{\mathrm{1}+\mathrm{3}{x}^{\mathrm{2}} }\:{dx}\:. \\ $$ Commented by…

let-A-n-0-e-nx-2-sin-x-n-dx-with-n-integr-not-0-1-calculate-A-n-2-find-lim-n-A-n-

Question Number 37285 by math khazana by abdo last updated on 11/Jun/18 $${let}\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−{nx}^{\mathrm{2}} } {sin}\left(\frac{{x}}{{n}}\right){dx}\:\:{with}\:{n}\:{integr}\:{not}\:\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \\ $$…

let-U-n-0-1-x-n-1-x-2n-1-dx-1-find-a-equivalent-of-U-n-n-2-study-the-comvergence-of-U-n-

Question Number 168355 by Mathspace last updated on 08/Apr/22 $$\left.{let}\:{U}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \left({x}^{{n}} \right)\sqrt{\mathrm{1}−{x}^{\mathrm{2}{n}+\mathrm{1}} }\right){dx} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{equivalent}\:{of}\:{U}_{{n}} \left({n}\sim\infty\right) \\ $$$$\left.\mathrm{2}\right)\:{study}\:{the}\:{comvergence}\:{of}\:\Sigma\:{U}_{{n}} \\ $$ Answered by Mathspace…