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Category: Integration

Question-171253

Question Number 171253 by vonem1 last updated on 11/Jun/22 Answered by haladu last updated on 11/Jun/22 $$\:\mathrm{8}\int_{\mathrm{1}} ^{\mathrm{4}} \:\boldsymbol{\mathrm{t}}^{−\frac{\mathrm{1}}{\mathrm{2}}} \:\:\:\:\boldsymbol{\mathrm{dt}}\:−\mathrm{12}\:\:\int\:\boldsymbol{\mathrm{t}}^{\frac{\mathrm{3}}{\mathrm{2}}} \:\:\boldsymbol{\mathrm{dt}} \\ $$$$\:\:\: \\ $$$$\:\:\mathrm{8}\:\:\:\frac{\boldsymbol{\mathrm{t}}^{−\frac{\mathrm{1}}{\mathrm{2}}\:+\mathrm{1}}…

let-A-n-0-1-x-2n-1-ln-x-x-2-1-dx-1-justify-the-existence-of-A-n-2-calculate-A-n-1-A-n-3-prove-that-x-0-1-0-lt-xln-x-x-2-1-lt-1-2-4-find-lim-n-A-n-

Question Number 40158 by maxmathsup by imad last updated on 16/Jul/18 $${let}\:\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{x}^{\mathrm{2}{n}+\mathrm{1}} \:{ln}\left({x}\right)}{{x}^{\mathrm{2}} \:−\mathrm{1}}{dx} \\ $$$$\left.\mathrm{1}\right)\:{justify}\:{the}\:{existence}\:{of}\:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right){calculate}\:{A}_{{n}+\mathrm{1}} \:−{A}_{{n}} \\ $$$$\left.\mathrm{3}\left.\right)\:{prove}\:{that}\:\:{x}\in\right]\mathrm{0},\mathrm{1}\left[\:\Rightarrow\mathrm{0}<\frac{{xln}\left({x}\right)}{{x}^{\mathrm{2}} \:−\mathrm{1}}<\frac{\mathrm{1}}{\mathrm{2}}\:\:\right.…

let-I-n-0-dx-1-x-3-n-find-a-relation-etween-I-n-and-I-n-1-2-calculate-I-1-and-I-2-

Question Number 40159 by maxmathsup by imad last updated on 16/Jul/18 $${let}\:{I}_{{n}} =\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{3}} \right)^{{n}} } \\ $$$${find}\:{a}\:{relation}\:{etween}\:{I}_{{n}} \:{and}\:{I}_{{n}+\mathrm{1}} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{I}_{\mathrm{1}\:} \:{and}\:{I}_{\mathrm{2}} \\ $$…