Menu Close

Category: Integration

let-A-n-0-1-x-n-e-x-dx-1-calculate-A-1-and-A-2-2-prove-that-A-n-1-n-1-A-n-1-e-3-calculate-A-3-A-4-and-A-5-4-calculate-I-0-1-x-3-2x-2-x-e-x-dx-

Question Number 40136 by maxmathsup by imad last updated on 16/Jul/18 $${let}\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{x}^{{n}} \:{e}^{−{x}} {dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{\mathrm{1}} \:\:\:{and}\:{A}_{\mathrm{2}} \\ $$$$\left.\mathrm{2}\right)\:{prove}\:{that}\:\:\:{A}_{{n}+\mathrm{1}} =\left({n}+\mathrm{1}\right){A}_{{n}} \:−\frac{\mathrm{1}}{{e}} \\…