integral from 0 to 5 of x^2-3x-4

解

\int_{0}^{5} x^{2} - 3 x - 4 d x

- \frac{95}{6}

十進法表記

- 15.83333 \dots

解答ステップ

\int_{0}^{5} x^{2} - 3 x - 4 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}^{5} x^{2} d x - \int_{0}^{5} 3 x d x - \int_{0}^{5} 4 d x

\int_{0}^{5} x^{2} d x = \frac{125}{3}

\int_{0}^{5} 3 x d x = \frac{75}{2}

\int_{0}^{5} 4 d x = 20

= \frac{125}{3} - \frac{75}{2} - 20

簡素化

\frac{125}{3} - \frac{75}{2} - 20 : - \frac{95}{6}

= - \frac{95}{6}