integral from 0 to 1 of (x)-(x^2)

解

\int_{0}^{1} (x) - (x^{2}) d x

\frac{1}{6}

十進法表記

0.16666 \dots

解答ステップ

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

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

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

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

簡素化

\frac{1}{2} - \frac{1}{3} : \frac{1}{6}

= \frac{1}{6}