integral from 0 to 3 of t^2-t-6

解

\int_{0}^{3} t^{2} - t - 6 d t

- \frac{27}{2}

十進法表記

- 13.5

解答ステップ

\int_{0}^{3} t^{2} - t - 6 d t

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} t^{2} d t - \int_{0}^{3} t d t - \int_{0}^{3} 6 d t

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

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

\int_{0}^{3} 6 d t = 18

= 9 - \frac{9}{2} - 18

簡素化

9 - \frac{9}{2} - 18 : - \frac{27}{2}

= - \frac{27}{2}