integral from-100 to 0 of-2ax

解答

\int_{- 100}^{0} - 2 a x d x

10000 a

求解步骤

\int_{- 100}^{0} - 2 a x d x

提出常数:

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

= - 2 a \cdot \int_{- 100}^{0} x d x

使用幂法则

= - 2 a [\frac{x ^{2}}{2}]_{- 100}^{0}

带入上下限计算后得:

- 5000

= - 2 a (- 5000)

化简

= 10000 a

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