integral from 1 to 9 of 7sqrt(u)

解答

\int_{1}^{9} 7 u d u

\frac{364}{3}

十进制

121.33333 \dots

求解步骤

\int_{1}^{9} 7 u d u

提出常数:

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

= 7 \cdot \int_{1}^{9} u d u

使用幂法则

= 7 [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{9}

带入上下限计算后得:

\frac{52}{3}

= 7 \cdot \frac{52}{3}

化简

= \frac{364}{3}

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