Question Number 205506 by Lindemann last updated on 23/Mar/24
$$\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}−{x}^{\mathrm{4}} }{dx} \\ $$
Answered by sniper237 last updated on 23/Mar/24
$$\overset{{u}={x}^{\mathrm{4}} } {=}\frac{\mathrm{1}}{\mathrm{4}}\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}−{u}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} {u}^{\frac{\mathrm{1}}{\mathrm{4}}−\mathrm{1}} {du}=\frac{\mathrm{1}}{\mathrm{4}}{Beta}\left(\frac{\mathrm{1}}{\mathrm{4}};\frac{\mathrm{3}}{\mathrm{2}}\right) \\ $$