integral from 0 to 1 of sqrt(2x)

解答

\int_{0}^{1} 2 x d x

- \frac{2}{3} + 2

十进制

0.94280 \dots

求解步骤

\int_{0}^{1} 2 x d x

使用分布积分法

= [2 x x - \int \frac{x}{2} d x]_{0}^{1}

\int \frac{x}{2} d x = \frac{2}{3} x^{\frac{3}{2}}

= [2 x x - \frac{2}{3} x^{\frac{3}{2}}]_{0}^{1}

带入上下限计算后得:

- \frac{2}{3} + 2

= - \frac{2}{3} + 2

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