integral from 0 to 7 of |x^2-6x+5|

解

\int_{0}^{7} x^{2} - 6 x + 5 d x

\frac{71}{3}

十進法表記

23.66666 \dots

解答ステップ

\int_{0}^{7} x^{2} - 6 x + 5 d x

絶対数を排除する

= \int_{0}^{1} x^{2} - 6 x + 5 d x + \int_{1}^{5} - x^{2} + 6 x - 5 d x + \int_{5}^{7} x^{2} - 6 x + 5 d x

\int_{0}^{1} x^{2} - 6 x + 5 d x = \frac{7}{3}

\int_{1}^{5} - x^{2} + 6 x - 5 d x = \frac{32}{3}

\int_{5}^{7} x^{2} - 6 x + 5 d x = \frac{32}{3}

= \frac{7}{3} + \frac{32}{3} + \frac{32}{3}

簡素化

\frac{7}{3} + \frac{32}{3} + \frac{32}{3} : \frac{71}{3}

= \frac{71}{3}