Intuition behind centre of mass equation for a rigid body

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Pochen Liu
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Homework Statement
I don't understand how we move from the discrete equation to the continuous one
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I don't know how to type this in
So my basic understanding of an integral is that it finds the area underneath a graph.

I understand the idea behind an integral being the summation of f(x) * delta x, where delta x approaches zero.

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If I look at the integral it's telling me that there's a change in mass that is being multiplied by its displacement?
Supposedly it's meant to represent a uniform distribution but I can't see it. If someone could clear up my intuition behind this that would be great :)
 
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Pochen Liu said:
change in mass that is being multiplied by its displacement?
No, it is an element of mass multiplied by its displacement from the origin.

Pochen Liu said:
it's meant to represent a uniform distribution
No, it is quite general.