integral from 4 to 6 of t^2-2t-8

解

\int_{4}^{6} t^{2} - 2 t - 8 d t

\frac{44}{3}

十進法表記

14.66666 \dots

解答ステップ

\int_{4}^{6} t^{2} - 2 t - 8 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_{4}^{6} t^{2} d t - \int_{4}^{6} 2 t d t - \int_{4}^{6} 8 d t

\int_{4}^{6} t^{2} d t = \frac{152}{3}

\int_{4}^{6} 2 t d t = 20

\int_{4}^{6} 8 d t = 16

= \frac{152}{3} - 20 - 16

簡素化

\frac{152}{3} - 20 - 16 : \frac{44}{3}

= \frac{44}{3}