6.1 Areas Between Curves/11

File:Angel's.png

$y=x^{2}\qquad y={\sqrt {x}}$

$\int _{0}^{1}({\sqrt {x}}-x^{2})=[{\frac {2}{3}}x^{\frac {3}{2}}-{\frac {x^{3}}{3}}]$

$={\frac {2}{3}}(1)^{\frac {3}{2}}-{\frac {(1)^{3}}{3}}={\frac {1}{3}}$