integral from 0 to 1 of x^{1/2}-x^2

解

\int_{0}^{1} x^{\frac{1}{2}} - x^{2} d x

\frac{1}{3}

十進法表記

0.33333 \dots

解答ステップ

\int_{0}^{1} x^{\frac{1}{2}} - x^{2} d x

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{1} x^{\frac{1}{2}} d x - \int_{0}^{1} x^{2} d x

\int_{0}^{1} x^{\frac{1}{2}} d x = \frac{2}{3}

\int_{0}^{1} x^{2} d x = \frac{1}{3}

= \frac{2}{3} - \frac{1}{3}

簡素化

\frac{2}{3} - \frac{1}{3} : \frac{1}{3}

= \frac{1}{3}