integral from 3 to 5 of x^{3/2}

解答

\int_{3}^{5} x^{\frac{3}{2}} d x

10 \cdot 5^{\frac{1}{2}} - \frac{18 \cdot 3 ^{\frac{1}{2}}}{5}

十进制

16.12529 \dots

求解步骤

\int_{3}^{5} x^{\frac{3}{2}} d x

使用幂法则

= [\frac{2}{5} x^{\frac{5}{2}}]_{3}^{5}

带入上下限计算后得:

10 \cdot 5^{\frac{1}{2}} - \frac{18 \cdot 3 ^{\frac{1}{2}}}{5}

= 10 \cdot 5^{\frac{1}{2}} - \frac{18 \cdot 3 ^{\frac{1}{2}}}{5}

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