integral from 0 to s of 3e^x

解答

\int_{0}^{s} 3 e^{x} d x

3 (e^{s} - 1)

求解步骤

\int_{0}^{s} 3 e^{x} d x

提出常数:

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

= 3 \cdot \int_{0}^{s} e^{x} d x

使用积分常见定则:

\int e^{x} d x = e^{x}

= 3 [e^{x}]_{0}^{s}

带入上下限计算后得:

e^{s} - 1

= 3 (e^{s} - 1)

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