integral from 0 to 2 of (6-t)sqrt(t)

解

\int_{0}^{2} (6 - t) t d t

82 - \frac{8 2}{5}

十進法表記

9.05096 \dots

解答ステップ

\int_{0}^{2} (6 - t) t d t

拡張

(6 - t) t : 6 t - t^{\frac{3}{2}}

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

\int_{0}^{2} 6 t d t = 82

\int_{0}^{2} t^{\frac{3}{2}} d t = \frac{8 2}{5}

= 82 - \frac{8 2}{5}