integral from 0 to 7 of 2t^2-20t+48

解

\int_{0}^{7} 2 t^{2} - 20 t + 48 d t

\frac{224}{3}

十進法表記

74.66666 \dots

解答ステップ

\int_{0}^{7} 2 t^{2} - 20 t + 48 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}^{7} 2 t^{2} d t - \int_{0}^{7} 20 t d t + \int_{0}^{7} 48 d t

\int_{0}^{7} 2 t^{2} d t = \frac{686}{3}

\int_{0}^{7} 20 t d t = 490

\int_{0}^{7} 48 d t = 336

= \frac{686}{3} - 490 + 336

簡素化

\frac{686}{3} - 490 + 336 : \frac{224}{3}

= \frac{224}{3}