y = x 2 y = x {\displaystyle y=x^{2}\qquad y={\sqrt {x}}} ∫ 0 1 ( x − x 2 ) = [ 2 3 x 3 2 − x 3 3 ] {\displaystyle \int _{0}^{1}({\sqrt {x}}-x^{2})=[{\frac {2}{3}}x^{\frac {3}{2}}-{\frac {x^{3}}{3}}]} = 2 3 ( 1 ) 3 2 − ( 1 ) 3 3 = 1 3 {\displaystyle ={\frac {2}{3}}(1)^{\frac {3}{2}}-{\frac {(1)^{3}}{3}}={\frac {1}{3}}}
![{\displaystyle \int _{0}^{1}({\sqrt {x}}-x^{2})=[{\frac {2}{3}}x^{\frac {3}{2}}-{\frac {x^{3}}{3}}]}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/e4827f82848bdfcacb5d71146514f17cd74d9b8f)
