integral from 0 to 0.5 of 500x

解答

\int_{0}^{0.5} 500 x d x

62.5

求解步骤

\int_{0}^{0.5} 500 x d x

提出常数:

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

= 500 \cdot \int_{0}^{0.5} x d x

使用幂法则

= 500 [\frac{x ^{2}}{2}]_{0}^{0.5}

化简

= 500 [0.5 x^{2}]_{0}^{0.5}

带入上下限计算后得:

0.125

= 500 \cdot 0.125

化简

= 62.5

\int_{0}^{16} x e^{- x} d x

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