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## Main Question or Discussion Point

Hello,

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.

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.