integral from 1 to 8 of (t^2-4t-12)

解

\int_{1}^{8} (t^{2} - 4 t - 12) d t

- \frac{119}{3}

十進法表記

- 39.66666 \dots

解答ステップ

\int_{1}^{8} t^{2} - 4 t - 12 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_{1}^{8} t^{2} d t - \int_{1}^{8} 4 t d t - \int_{1}^{8} 12 d t

\int_{1}^{8} t^{2} d t = \frac{511}{3}

\int_{1}^{8} 4 t d t = 126

\int_{1}^{8} 12 d t = 84

= \frac{511}{3} - 126 - 84

簡素化

\frac{511}{3} - 126 - 84 : - \frac{119}{3}

= - \frac{119}{3}