integral from 0 to 4 of-x^2-3x

解

\int_{0}^{4} - x^{2} - 3 x d x

- \frac{136}{3}

十進法表記

- 45.33333 \dots

解答ステップ

\int_{0}^{4} - x^{2} - 3 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_{0}^{4} x^{2} d x - \int_{0}^{4} 3 x d x

\int_{0}^{4} x^{2} d x = \frac{64}{3}

\int_{0}^{4} 3 x d x = 24

= - \frac{64}{3} - 24

簡素化

- \frac{64}{3} - 24 : - \frac{136}{3}

= - \frac{136}{3}