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## Homework Statement

I have a doubt about the steiner theorem demonstration, its actually trivial, but I can't realize why is this.

Lets see, the demonstration which you can see http://en.wikipedia.org/wiki/Parallel_axis_theorem" [Broken] goes as follows:

[tex]I_{cm} = \int{(x^2 + y^2)} dm[/tex]

[tex]I_z = \int{((x - r)^2 + y^2)} dm[/tex]

[tex]I_z = \int{(x^2 + y^2)} dm + r^2 \int dm - 2r\int{x} dm[/tex]

[tex]I_z = I_{cm} + mr^2[/tex]

What I need to know is why this gives zero:

[tex]2r\int{x} dm[/tex]

Bye there, and thanks for your help :)

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