integral from 0 to 8 of 2t^2-24t+70

解

\int_{0}^{8} 2 t^{2} - 24 t + 70 d t

\frac{400}{3}

十進法表記

133.33333 \dots

解答ステップ

\int_{0}^{8} 2 t^{2} - 24 t + 70 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}^{8} 2 t^{2} d t - \int_{0}^{8} 24 t d t + \int_{0}^{8} 70 d t

\int_{0}^{8} 2 t^{2} d t = \frac{1024}{3}

\int_{0}^{8} 24 t d t = 768

\int_{0}^{8} 70 d t = 560

= \frac{1024}{3} - 768 + 560

簡素化

\frac{1024}{3} - 768 + 560 : \frac{400}{3}

= \frac{400}{3}