integral from 0 to 1/2 ln(3) of e^{2x}

解答

\int_{0}^{\frac{1}{2} l n (3)} e^{2 x} d x

1

求解步骤

\int_{0}^{\frac{1}{2} l n (3)} e^{2 x} d x

使用换元积分法

= \int_{0}^{l n (3)} e^{u} \frac{1}{2} d u

提出常数:

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

= \frac{1}{2} \cdot \int_{0}^{l n (3)} e^{u} d u

使用积分常见定则:

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

= \frac{1}{2} [e^{u}]_{0}^{l n (3)}

带入上下限计算后得:

2

= \frac{1}{2} \cdot 2

化简

= 1

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