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[讲师] 我们已知一个黎曼和，

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求在n趋向于无穷大时它的极限。

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这个视频的目标是

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看看我们能否将它改写

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为一个定积分。

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在这里鼓励你暂停这个视频，

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尝试看看你能不能独立解决这个问题。

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现在让我们回忆一下，

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定积分是如何与黎曼积分关联起来的。

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那么如果我有从a到b，

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对f(x)dx的定积分。

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我们在其它的视频中看过了，

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这就等于

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当n趋向于无穷时的极限，求和符号，

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从i等于1，到n，

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本质上来说我们要求

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多个矩形的面积的和，

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其中每一个矩形的宽度

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我们可以写作Δx。

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所以每个矩形宽度等于Δx，

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然后高度

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就等于这个函数

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在Δx某个部分的值。

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如果我们求右黎曼和，

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我们就可以取矩形的右边，

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或者说这个区间的最右边的点。

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所以，我们从下限a开始，

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然后我们在这之上加相应个数的Δx。

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如果i等于1，

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我们就加上一个Δx。

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也就是在第一个矩形的右边。

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如果i等于2，我们就加上两个Δx。

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所以这就是Δx

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乘以i。

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