integral from-1 to 0 of x^3-x^2-2x

解

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

\frac{5}{12}

十進法表記

0.41666 \dots

解答ステップ

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

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

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

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

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

簡素化

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

= \frac{5}{12}