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I'm reading Mathematical Methods in the physical sciences by Mary Boas and in it, she defines the center of mass of a body in 3 dimensions

[tex] \int \overline {x}dM=\int xdM [/tex]

[tex] \int \overline {y}dM=\int ydM [/tex]

[tex] \int \overline {z}dM=\int zdM [/tex]

In standard undergraduate textbooks, I've always seen it written as

[tex] \overline {X}=\dfrac {1} {M}\int xdM [/tex]

I guess I don't understand the reasoning behind defining it the way she did. I know that [tex]\overline {x} [/tex] is constant so you can pull it out and you'd just simply get the [tex] \int dM [/tex], leaving you with the formula that is generally seen in undergraduate texts.

But why write the formula as she did to begin with. Is there a particular benefit to doing so?

Any insight would be great, thanks.