来自《耶鲁大学开放课程：基础物理第6集第6集》

if I did the work done by the force along that segment,

如果力沿着这一段路径做功
what is the integral of F·dr?

F·dr 的积分是多少
So, let's take a tiny portion of that,

让我们取这条线段上的一小段
looks like this, right,

就像这样
that's dr, it's got a dx, and it's got a dy.

这就是 dr 有个 dx 有个 dy
Now, you notice that as this segment becomes very small

现在注意到这一段变化很小
dy / dx is a slope;

dy / dx 是斜率
therefore, dy will be dy / dx times dx.

因此 dy 就等于 dy / dx 乘以 dx
In other words, dx and dy are not independent

就是说如果物体向某个特定方向移动
if they're moving in a particular direction.

dx 和 dy 是相关的
I hope you understand that.

我希望你们能明白这一点
You want to follow a certain curve.

你想沿着某条曲线运动