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人気のある微分積分 >

integral from-2 to 2 of x|x^2-1|

解

\int_{- 2}^{2} x x^{2} - 1 d x

解

0

解答ステップ

\int_{- 2}^{2} x x^{2} - 1 d x

絶対数を排除する

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

\int_{- 2}^{- 1} x (x^{2} - 1) d x = - \frac{9}{4}

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

\int_{1}^{2} x (x^{2} - 1) d x = \frac{9}{4}

= - \frac{9}{4} + 0 + \frac{9}{4}

簡素化

= 0

グラフ

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