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Category: Integration

1-pi-determinant-x-3-lnx-sinx-3x-2-1-x-cosx-6-2x-3-cosx-dx-

Question Number 128385 by n0y0n last updated on 06/Jan/21 $$\int_{\mathrm{1}} ^{\:\pi} \begin{vmatrix}{\mathrm{x}^{\mathrm{3}} }&{\mathrm{lnx}}&{\mathrm{sinx}}\\{\mathrm{3x}^{\mathrm{2}} }&{\frac{\mathrm{1}}{\mathrm{x}}}&{\mathrm{cosx}}\\{\mathrm{6}}&{\mathrm{2x}^{−\mathrm{3}} }&{−\mathrm{cosx}}\end{vmatrix}\mathrm{dx}\:=?\: \\ $$ Answered by mathmax by abdo last updated on…

Question-62826

Question Number 62826 by Cheyboy last updated on 25/Jun/19 Commented by mathmax by abdo last updated on 25/Jun/19 $$\left.{b}\right)\:{I}\:=\int_{\mathrm{0}} ^{\pi} \:\:\frac{{sin}\theta}{\:\sqrt{\pi−\theta}}\:\:{changement}\sqrt{\pi−\theta}\:={x}\:{give}\:{I}\:=\int_{\sqrt{\pi}} ^{\mathrm{0}} \:\frac{{sin}\left(\pi−{x}^{\mathrm{2}} \right)}{{x}}\:\left(−\mathrm{2}{x}\right){dx} \\…

let-U-n-0-cos-ch-nx-3-x-2-2-dx-1-calculate-U-n-interms-of-n-2-find-lim-n-n-U-n-and-lim-n-n-2-U-n-3-study-the-serie-U-n-

Question Number 62828 by mathmax by abdo last updated on 25/Jun/19 $${let}\:{U}_{{n}} =\int_{\mathrm{0}} ^{+\infty} \:\:\frac{{cos}\left({ch}\left({nx}\right)\right)}{\left(\mathrm{3}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{U}_{{n}} \:{interms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{n}\:{U}_{{n}} \:\:\:\:\:{and}\:{lim}_{{n}\rightarrow+\infty} \:{n}^{\mathrm{2}}…

let-U-n-0-arctan-nt-1-n-2-t-2-dt-with-n-natural-1-1-calculate-U-n-2-calculate-lim-n-n-2-U-n-3-study-the-convergence-of-U-n-

Question Number 62812 by mathmax by abdo last updated on 25/Jun/19 $${let}\:{U}_{{n}} =\int_{\mathrm{0}} ^{+\infty} \:\:\frac{{arctan}\left({nt}\right)}{\mathrm{1}+{n}^{\mathrm{2}} {t}^{\mathrm{2}} }{dt}\:\:\:\:{with}\:{n}\:{natural}\geqslant\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{U}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{lim}_{{n}\rightarrow+\infty} \:{n}^{\mathrm{2}} \:{U}_{{n}} \\ $$$$\left.\mathrm{3}\right)\:{study}\:{the}\:{convergence}\:{of}\:\Sigma\:{U}_{{n}}…

1-find-2x-2-1-x-1-x-3-x-2-x-2-dx-2-calculate-5-2x-2-1-x-1-x-3-x-2-x-2-dx-

Question Number 62811 by mathmax by abdo last updated on 25/Jun/19 $$\left.\mathrm{1}\right)\:{find}\:\:\int\:\:\:\frac{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{1}}{\left({x}+\mathrm{1}\right)\left({x}−\mathrm{3}\right)\left({x}^{\mathrm{2}} −{x}+\mathrm{2}\right)}{dx} \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{5}} ^{+\infty} \:\:\:\:\frac{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{1}}{\left({x}+\mathrm{1}\right)\left({x}−\mathrm{3}\right)\left({x}^{\mathrm{2}} −{x}+\mathrm{2}\right)}{dx} \\ $$ Commented by Prithwish…