线积分计算的思路
线积分计算的思路主要是：将矢量函数\(\mathbf{F}(\mathbf{r})\)通过路径曲线\(C\)参数化得到的\(\mathbf{r}(t)\)转化成标量函数\(f(t)\)，此时原线积分即可转化为普通的标量积分。例如假设\(\mathbf{F}(\mathbf{r})\)是一个空间中的电场，\(C\)是质点在电场中的路径曲线，则原线积分相当于在计算质点在电场\(\mathbf{F}(\mathbf{r})\)中沿路径\(C\)行进时做的功之和，而转化后的标量积分相当于从质点的角度在时域中计算，求得每一时刻\(t\)质点做的功，最后计算总功。
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