integral from-1 to 2 of (|x|(x^2-1))/x

解

\int_{- 1}^{2} \frac{∣ x ∣ ( x ^{2} - 1 )}{x} d x

\frac{4}{3}

十進法表記

1.33333 \dots

解答ステップ

\int_{- 1}^{2} \frac{∣ x ∣ ( x ^{2} - 1 )}{x} d x

絶対数を排除する

= \int_{- 1}^{0} \frac{( - x ) ( x ^{2} - 1 )}{x} d x + \int_{0}^{2} \frac{x ( x ^{2} - 1 )}{x} d x

\int_{- 1}^{0} \frac{( - x ) ( x ^{2} - 1 )}{x} d x = \frac{2}{3}

\int_{0}^{2} \frac{x ( x ^{2} - 1 )}{x} d x = \frac{2}{3}

= \frac{2}{3} + \frac{2}{3}

簡素化

\frac{2}{3} + \frac{2}{3} : \frac{4}{3}

= \frac{4}{3}