integral from-3 to 4 of |x^2-4|

解

\int_{- 3}^{4} x^{2} - 4 d x

\frac{71}{3}

十進法表記

23.66666 \dots

解答ステップ

\int_{- 3}^{4} x^{2} - 4 d x

絶対数を排除する

= \int_{- 3}^{- 2} x^{2} - 4 d x + \int_{- 2}^{2} - x^{2} + 4 d x + \int_{2}^{4} x^{2} - 4 d x

\int_{- 3}^{- 2} x^{2} - 4 d x = \frac{7}{3}

\int_{- 2}^{2} - x^{2} + 4 d x = \frac{32}{3}

\int_{2}^{4} x^{2} - 4 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}