来自《耶鲁大学开放课程：基础物理 第5集 第5集》

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  then the change in kinetic energy will be then F of x times Δx.
  那么动能变化量就等于 F(x) · Δx
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  Then, you wait a little longer, you go to a new place,
  然后你再等一会 来到一个新的位置
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  then you've got a new value of the force, maybe somewhere here.
  会有一个不同的力 也许在这里
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  Then, that times Δx is the work done in that region.
  这里的力乘 Δx 就是在这个区间里做的功
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  But geometrically,
  但就几何上来说
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  F times Δx is the area of the little rectangle
  F · Δx 等于这个小矩形的面积
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  whose base is Δx and whose height is the function F at that time.
  底为 Δx 高为对应时刻的 F
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  So, if you eventually went from here to here ,
  所以如果你最后从这里走到这里
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  let me call that point as x1 and let me call the ending point as x2,
  我们把这点叫 x1 把终点叫 x2
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  then the work done by you is really given by the area under that graph.
  那么你做的功就等于曲线下方的面积
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  And in every segment you pick up the change in kinetic energy,
  然后你把每一段的动能变化量
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  you add it all up.
  加起来