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

解

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

- \frac{11}{12}

十進法表記

- 0.91666 \dots

解答ステップ

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

拡張

x^{2} (x - 2) : x^{3} - 2 x^{2}

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

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

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

= - \frac{1}{4} - \frac{2}{3}

簡素化

- \frac{1}{4} - \frac{2}{3} : - \frac{11}{12}

= - \frac{11}{12}