我们称之为线积分与积分路径无关。

We say that the line integral is path independent.

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一个向量场,如果定义在单连通区域并且旋度为零，那么它就是一个梯度场，并且其上的线积分与路径无关。

OK, so, we've seen that if we have a vector field defined in a simply connected region, and its curl is zero, then it's a gradient field, and the line integral is path independent.

youdao

根本上说，以下性质是等价的，一个向量场是梯度场，等价于积分与路径无关，也等价于向量场是保守的。

And, basically, we say that these properties are equivalent being a gradient field or being path independent or being conservative.

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