Finding coordinates of the centroid

SUchica10
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Sketch the region bounded by the curves and visually estimate the location of the centroid. Then find the exact coordinates of the centroid.

y=1/x, y=0, x=1, x=2
 
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what's your definition of the centroid?
 
I am thinking it is the center of mass.
 
As robphy said, start with a definition.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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