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

解答

\int_{0}^{2} (x + 1)^{\frac{2}{3}} d x

\frac{9 \cdot 3 ^{\frac{2}{3}} - 3}{5}

十进制

3.14415 \dots

求解步骤

\int_{0}^{2} (x + 1)^{\frac{2}{3}} d x

使用换元积分法

= \int_{1}^{3} u^{\frac{2}{3}} d u

使用幂法则

= [\frac{3}{5} u^{\frac{5}{3}}]_{1}^{3}

带入上下限计算后得:

\frac{9 \cdot 3 ^{\frac{2}{3}}}{5} - \frac{3}{5}

= \frac{9 \cdot 3 ^{\frac{2}{3}}}{5} - \frac{3}{5}

化简

= \frac{9 \cdot 3 ^{\frac{2}{3}} - 3}{5}

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