integral from 0 to 8/9 of 8x-9x^2

解

\int_{0}^{\frac{8}{9}} 8 x - 9 x^{2} d x

\frac{256}{243}

十進法表記

1.05349 \dots

解答ステップ

\int_{0}^{\frac{8}{9}} 8 x - 9 x^{2} d x

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}^{\frac{8}{9}} 8 x d x - \int_{0}^{\frac{8}{9}} 9 x^{2} d x

\int_{0}^{\frac{8}{9}} 8 x d x = \frac{256}{81}

\int_{0}^{\frac{8}{9}} 9 x^{2} d x = \frac{512}{243}

= \frac{256}{81} - \frac{512}{243}

簡素化

\frac{256}{81} - \frac{512}{243} : \frac{256}{243}

= \frac{256}{243}