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 Number 128373 by BHOOPENDRA last updated on 06/Jan/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} \:{x}^{\frac{\mathrm{3}}{\mathrm{2}}} \left(\mathrm{1}−{x}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} \:{dx} \\ $$ Answered by Dwaipayan Shikari last updated on 06/Jan/21 $$\int_{\mathrm{0}}…
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Question Number 62833 by aliesam last updated on 25/Jun/19 $$\int\frac{{cos}\left({x}\right)}{{x}}\:{dx} \\ $$$$ \\ $$$$\int\sqrt{{sin}\left({x}\right)\:}\:{dx} \\ $$$$ \\ $$$$\int\sqrt{\mathrm{1}−{k}^{\mathrm{2}} {sin}^{\mathrm{2}} \left({x}\right)}\:{dx}\:\:\:\:\:\:{k}:{constant} \\ $$ Commented by mathmax…
Question Number 62826 by Cheyboy last updated on 25/Jun/19 Commented by mathmax by abdo last updated on 25/Jun/19 $$\left.{b}\right)\:{I}\:=\int_{\mathrm{0}} ^{\pi} \:\:\frac{{sin}\theta}{\:\sqrt{\pi−\theta}}\:\:{changement}\sqrt{\pi−\theta}\:={x}\:{give}\:{I}\:=\int_{\sqrt{\pi}} ^{\mathrm{0}} \:\frac{{sin}\left(\pi−{x}^{\mathrm{2}} \right)}{{x}}\:\left(−\mathrm{2}{x}\right){dx} \\…
Question Number 62828 by mathmax by abdo last updated on 25/Jun/19 $${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} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{U}_{{n}} \:{interms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{n}\:{U}_{{n}} \:\:\:\:\:{and}\:{lim}_{{n}\rightarrow+\infty} \:{n}^{\mathrm{2}}…
Question Number 62814 by Cheyboy last updated on 25/Jun/19 Commented by Cheyboy last updated on 25/Jun/19 $${Please}\:{help}\:{me}\:{with}\:{these}\:{question} \\ $$ Commented by mathmax by abdo last…
Question Number 62813 by mathmax by abdo last updated on 25/Jun/19 $${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−\left({t}^{\mathrm{2}} \:+\frac{\mathrm{1}}{{t}^{\mathrm{2}} }\right)} {dt} \\ $$$${study}\:{first}\:{the}\:{convergence}\:. \\ $$ Terms of Service Privacy…
Question Number 62812 by mathmax by abdo last updated on 25/Jun/19 $${let}\:{U}_{{n}} =\int_{\mathrm{0}} ^{+\infty} \:\:\frac{{arctan}\left({nt}\right)}{\mathrm{1}+{n}^{\mathrm{2}} {t}^{\mathrm{2}} }{dt}\:\:\:\:{with}\:{n}\:{natural}\geqslant\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{U}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{lim}_{{n}\rightarrow+\infty} \:{n}^{\mathrm{2}} \:{U}_{{n}} \\ $$$$\left.\mathrm{3}\right)\:{study}\:{the}\:{convergence}\:{of}\:\Sigma\:{U}_{{n}}…
Question Number 62811 by mathmax by abdo last updated on 25/Jun/19 $$\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…