Question Number 65771 by mathmax by abdo last updated on 03/Aug/19
![let X_n =∫_0 ^(π/4) sin^n xdx 1) calculate X_0 ,X_1 ,X_2 ,X_3 2) find X_n interms of n 3)find the value of ∫_0 ^(π/4) sin^8 xdx](https://www.tinkutara.com/question/Q65771.png)
$${let}\:{X}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:{sin}^{{n}} {xdx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{X}_{\mathrm{0}} \:,{X}_{\mathrm{1}} \:,{X}_{\mathrm{2}} ,{X}_{\mathrm{3}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{X}_{{n}} {interms}\:{of}\:{n} \\ $$$$\left.\mathrm{3}\right){find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:{sin}^{\mathrm{8}} {xdx} \\ $$