integral from-1 to 8 of-x^2+7x+8

解

\int_{- 1}^{8} - x^{2} + 7 x + 8 d x

\frac{243}{2}

十進法表記

121.5

解答ステップ

\int_{- 1}^{8} - x^{2} + 7 x + 8 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}^{8} x^{2} d x + \int_{- 1}^{8} 7 x d x + \int_{- 1}^{8} 8 d x

\int_{- 1}^{8} x^{2} d x = 171

\int_{- 1}^{8} 7 x d x = \frac{441}{2}

\int_{- 1}^{8} 8 d x = 72

= - 171 + \frac{441}{2} + 72

簡素化

- 171 + \frac{441}{2} + 72 : \frac{243}{2}

= \frac{243}{2}