integral from 0 to 5 of v(t)

解答

\int_{0}^{5} v d t

\frac{25 v}{2}

求解步骤

\int_{0}^{5} v t d t

提出常数:

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

= v \cdot \int_{0}^{5} t d t

使用幂法则

= v [\frac{t ^{2}}{2}]_{0}^{5}

带入上下限计算后得:

\frac{25}{2}

= v \frac{25}{2}

化简

= \frac{25 v}{2}

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