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

解

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

- \frac{5}{6}

十進法表記

- 0.83333 \dots

解答ステップ

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

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

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

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

簡素化

- \frac{1}{2} - \frac{1}{3} : - \frac{5}{6}

= - \frac{5}{6}