integral from 1 to 4 of 63x^{5/2}

解答

\int_{1}^{4} 63 x^{\frac{5}{2}} d x

2286

求解步骤

\int_{1}^{4} 63 x^{\frac{5}{2}} d x

提出常数:

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

= 63 \cdot \int_{1}^{4} x^{\frac{5}{2}} d x

使用幂法则

= 63 [\frac{2}{7} x^{\frac{7}{2}}]_{1}^{4}

带入上下限计算后得:

\frac{254}{7}

= 63 \cdot \frac{254}{7}

化简

= 2286

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