Question Number 156138 by SANOGO last updated on 08/Oct/21
$${la}\:{valeur}\:{de}\:{l}'{integrale} \\ $$$$\underset{{o}} {\int}^{\mathrm{1}} {x}\sqrt{\sqrt{\sqrt{{x}}}} \\ $$$$ \\ $$
Commented by cortano last updated on 08/Oct/21
![∫_0 ^1 x.x^(1/8) dx=∫_0 ^1 x^(9/8) dx = (8/(17)) [ x^(17/8) ]_0 ^1 = (8/(17))](https://www.tinkutara.com/question/Q156139.png)
$$\int_{\mathrm{0}} ^{\mathrm{1}} {x}.{x}^{\mathrm{1}/\mathrm{8}} \:{dx}=\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{\mathrm{9}/\mathrm{8}} \:{dx} \\ $$$$=\:\frac{\mathrm{8}}{\mathrm{17}}\:\left[\:{x}^{\mathrm{17}/\mathrm{8}} \:\right]_{\mathrm{0}} ^{\mathrm{1}} \:=\:\frac{\mathrm{8}}{\mathrm{17}} \\ $$