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

解

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

65

解答ステップ

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

絶対数を排除する

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

\int_{- 5}^{- 3} x^{2} + x - 6 d x = \frac{38}{3}

\int_{- 3}^{2} - x^{2} - x + 6 d x = \frac{125}{6}

\int_{2}^{5} x^{2} + x - 6 d x = \frac{63}{2}

= \frac{38}{3} + \frac{125}{6} + \frac{63}{2}

簡素化

\frac{38}{3} + \frac{125}{6} + \frac{63}{2} : 65

= 65