integral from-12 to 12 of (144-x^2)

解答

\int_{- 12}^{12} (144 - x^{2}) d x

2304

求解步骤

\int_{- 12}^{12} 144 - 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

= \int_{- 12}^{12} 144 d x - \int_{- 12}^{12} x^{2} d x

\int_{- 12}^{12} 144 d x = 3456

\int_{- 12}^{12} x^{2} d x = 1152

= 3456 - 1152

化简

= 2304

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