integral from-h to h of (y^2-h^2)

解答

\int_{- h}^{h} (y^{2} - h^{2}) d y

\frac{2 h ^{3}}{3} - 2 h^{3}

求解步骤

\int_{- h}^{h} y^{2} - h^{2} d y

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{- h}^{h} y^{2} d y - \int_{- h}^{h} h^{2} d y

\int_{- h}^{h} y^{2} d y = \frac{2 h ^{3}}{3}

\int_{- h}^{h} h^{2} d y = 2 h^{3}

= \frac{2 h ^{3}}{3} - 2 h^{3}

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