integral of 1/486 (81-x^2)

解答

\int \frac{1}{486} (81 - x^{2}) d x

\frac{1}{486} (81 x - \frac{x ^{3}}{3}) + C

求解步骤

\int \frac{1}{486} (81 - x^{2}) d x

提出常数:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{486} \cdot \int 81 - x^{2} d x

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

= \frac{1}{486} (\int 81 d x - \int x^{2} d x)

\int 81 d x = 81 x

\int x^{2} d x = \frac{x ^{3}}{3}

= \frac{1}{486} (81 x - \frac{x ^{3}}{3})

解答补常数

= \frac{1}{486} (81 x - \frac{x ^{3}}{3}) + C

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