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Category: Integration

let-U-n-1-n-2-n-x-1-x-dx-with-n-3-1-calculate-and-determine-lim-n-U-n-2-study-the-convergence-of-U-n-

Question Number 65004 by mathmax by abdo last updated on 24/Jul/19 $${let}\:{U}_{{n}} =\:\int_{\frac{\mathrm{1}}{{n}}} ^{\frac{\mathrm{2}}{{n}}} \:\Gamma\left({x}\right)\Gamma\left(\mathrm{1}−{x}\right){dx}\:\:\:\:{with}\:{n}\geqslant\mathrm{3} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{and}\:{determine}\:{lim}_{{n}\rightarrow+\infty} \:{U}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{study}\:{the}\:{convergence}\:{of}\:\Sigma\:{U}_{{n}} \\ $$ Commented by mathmax…

let-f-x-x-7-arctan-2x-1-calculate-f-4-0-and-f-7-0-2-calculate-f-5-1-

Question Number 130534 by mathmax by abdo last updated on 26/Jan/21 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{7}} \:\mathrm{arctan}\left(\mathrm{2x}\right) \\ $$$$\left.\mathrm{1}\right)\mathrm{calculate}\:\:\mathrm{f}^{\left(\mathrm{4}\right)} \left(\mathrm{0}\right)\:\mathrm{and}\:\mathrm{f}^{\left(\mathrm{7}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:\mathrm{calculate}\:\mathrm{f}^{\left(\mathrm{5}\right)} \left(\mathrm{1}\right) \\ $$ Answered by mathmax…

find-f-0-arctan-1-x-4-x-2-dx-gt-0-and-determine-the-value-of-0-arctan-1-2x-x-2-4-dx-

Question Number 130532 by mathmax by abdo last updated on 26/Jan/21 $$\mathrm{find}\:\mathrm{f}\left(\alpha\right)=\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{arctan}\left(\mathrm{1}+\alpha\mathrm{x}\right)}{\mathrm{4}+\mathrm{x}^{\mathrm{2}} }\mathrm{dx}\:\:\:\left(\alpha>\mathrm{0}\right) \\ $$$$\mathrm{and}\:\mathrm{determine}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{arctan}\left(\mathrm{1}+\mathrm{2x}\right)}{\mathrm{x}^{\mathrm{2}} \:+\mathrm{4}}\mathrm{dx} \\ $$ Terms of Service…