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

解

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

\frac{1}{6}

十進法表記

0.16666 \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{1}{6}

= \frac{1}{6}