integral from-3 to 3 of |x|-(x^2-6)

解

\int_{- 3}^{3} ∣ x ∣ - (x^{2} - 6) d x

27

解答ステップ

\int_{- 3}^{3} ∣ x ∣ - (x^{2} - 6) d x

絶対数を排除する

= \int_{- 3}^{0} - x - (x^{2} - 6) d x + \int_{0}^{3} x - (x^{2} - 6) d x

\int_{- 3}^{0} - x - (x^{2} - 6) d x = \frac{27}{2}

\int_{0}^{3} x - (x^{2} - 6) d x = \frac{27}{2}

= \frac{27}{2} + \frac{27}{2}

簡素化

\frac{27}{2} + \frac{27}{2} : 27

= 27