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

解

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

- \frac{15}{2}

十進法表記

- 7.5

解答ステップ

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

\int_{0}^{3} x^{2} d x = 9

\int_{0}^{3} x d x = \frac{9}{2}

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

= - 9 + \frac{9}{2} - 3

簡素化

- 9 + \frac{9}{2} - 3 : - \frac{15}{2}

= - \frac{15}{2}