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.

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。

youdao

OK, so the claim is if I have a line integral to compute, that it doesn't matter which path I take b as long as it goes from point a to point b.

也就是，如果我需要计算一个线积分，无论我取怎样的路径,只要路径是从点a到点。

youdao

But the critical point is that commitments to maintain levels of aid are not an additional extra to the recovery agenda, but an integral element for its success.

但关键的一点是，维持援助水平并非经济复苏议程上的额外补充议题，它是经济复苏获得成功所不可或缺的一个要素。

youdao

We want to integrate. So let's take the integral of both sides, going from the initial point to the final point.

分别从初态,到末态做积分，消去微分。

麻省理工公开课 - 热力学与动力学课程节选

Some of what we went through were questions from last meeting, as I read out, the -- an update on the political situation, and an update on security force training -- meaning ANA and ANP -- Afghan National Army, Afghan National Police -- obviously integral in ensuring that at some point the Afghans are providing security for their own people.

WHITEHOUSE: 10/14/09: White House Press Briefing

It is really only in the past 50 years that plastic has become integral to our everyday lives, another point that makes me realize that we can vastly cut back our consumption of plastic if consumers weren't so lazy, and designer thought "smarter" early on in the manufacturing process.

CNN: STORY HIGHLIGHTS

Analysts are also making the point that Japanese-made components remain integral parts of products being assembled in China, Vietnam, and elsewhere.

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