integral from 0 to 3 of |5x-8|

解

\int_{0}^{3} ∣ 5 x - 8 ∣ d x

\frac{113}{10}

十進法表記

11.3

解答ステップ

\int_{0}^{3} ∣ 5 x - 8 ∣ d x

絶対数を排除する

= \int_{0}^{\frac{8}{5}} - 5 x + 8 d x + \int_{\frac{8}{5}}^{3} 5 x - 8 d x

\int_{0}^{\frac{8}{5}} - 5 x + 8 d x = \frac{32}{5}

\int_{\frac{8}{5}}^{3} 5 x - 8 d x = \frac{49}{10}

= \frac{32}{5} + \frac{49}{10}

簡素化

\frac{32}{5} + \frac{49}{10} : \frac{113}{10}

= \frac{113}{10}