integral from-1 to 0 of (2x+x^2-x^3)

解

\int_{- 1}^{0} (2 x + x^{2} - x^{3}) d x

- \frac{5}{12}

十進法表記

- 0.41666 \dots

解答ステップ

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

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

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

\int_{- 1}^{0} x^{3} d x = - \frac{1}{4}

= - 1 + \frac{1}{3} - (- \frac{1}{4})

簡素化

- 1 + \frac{1}{3} - (- \frac{1}{4}) : - \frac{5}{12}

= - \frac{5}{12}