我们称之为线积分与积分路径无关。
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.
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.
如果曲线c，起点为P0，终点为1，那么计算所做功的线积分，只与端点位置有关，而与我们选择的路径无关。
P1 If we have a curve c, from a point p0 to a point p1 then the line integral for work depends only on the end points and not on the actual path we chose.
那么这个证明，只需证出线积分与路径无关的，其它的也是用同样的方法。
OK, so the proof, so just going to prove that the line integral is path independent; the others work the same way.
其实是要对一个与其无关的向量场积分，其实是要对一个与其无关的向量场积分。
We are just integrating a vector field that has nothing to do with that.
而积分函数就是dxdy前的这个函数，它与积分边界无关。
While the function that you are integrating goes before the dx dy and not into the bounds or anything like that.
该研究表明夜间收缩压下降规律的丧失与移植肾功能差、慢性血管疾病积分高以及阻力指数高有关，而与移植肾纤维化无关。
This study indicates that lack of nocturnal fall in SBP is related to poor allograft function, high chronic vascular score, and high resistive index irrespective of allograft fibrosis.
积分在短时蠕变和长时间蠕变条件下是路往无关的，而在过渡蠕变时期，其与路径也只是弱相关。
The J integral is path-independent for the short time creep and long one, while in the transition period, it is weakly path-dependent.
本文把在单连通区域上成立的曲线积分与路线无关性定理推广到复连通区域。
In this paper the theorem in which a curve integral is independent of the integral path on a single connected region is generalized.
讨论了J积分的路径无关性和裂尖应力，应变奇异性。
A path independent of the J-integral and the stress, strain on the crack tip are discussed.
由于消元过程与消元次序无关，故可在此过程中引入2n类高精度时程积分方法。
Because the condensation process is not related to the condensation order, 2 N-type high precision time integration algorithm is introduced to the computational process.
利用与路径无关的M积分导出能量释放率表达式并给出相应的数值解。
The expression of energy release rate is deduced by means of the path-independent M-integral, and corresponding numerical results are given.
计算结果表明了焊接接头中J积分的路径无关性，并为焊接结构中弹塑性J积分的应用奠定了基础。
The results showed the path independence of J integral of welded joint. It established the foundation of application of elastic plastic J integral in welded structures.
计算结果表明了焊接接头中J积分的路径无关性，并为焊接结构中弹塑性J积分的应用奠定了基础。
The results showed the path independence of J integral of welded joint. It established the foundation of application of elastic plastic J integral in welded structures.
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