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

解

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

\frac{201}{10}

十進法表記

20.1

解答ステップ

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

拡張

(x^{2} - x - 3)^{2} : x^{4} - 2 x^{3} - 5 x^{2} + 6 x + 9

= \int_{- 1}^{2} x^{4} - 2 x^{3} - 5 x^{2} + 6 x + 9 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}^{2} x^{4} d x - \int_{- 1}^{2} 2 x^{3} d x - \int_{- 1}^{2} 5 x^{2} d x + \int_{- 1}^{2} 6 x d x + \int_{- 1}^{2} 9 d x

\int_{- 1}^{2} x^{4} d x = \frac{33}{5}

\int_{- 1}^{2} 2 x^{3} d x = \frac{15}{2}

\int_{- 1}^{2} 5 x^{2} d x = 15

\int_{- 1}^{2} 6 x d x = 9

\int_{- 1}^{2} 9 d x = 27

= \frac{33}{5} - \frac{15}{2} - 15 + 9 + 27

簡素化

\frac{33}{5} - \frac{15}{2} - 15 + 9 + 27 : \frac{201}{10}

= \frac{201}{10}