Help with Center of Mass (Calc II problem)

kiwwi
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Homework Statement


Find the centroid (center of mass) of the region in the first quadrant bounded by y=x, y=3x, x=n (>0)


Homework Equations





The Attempt at a Solution



No idea how to start the question, since I have to get the area of the region but
the graph does not intersect the second time. So it would be an area to inifinity.
 
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There are three lines.
 
The x boundaries of the region are x=0 and x=n, aren't they? There's a third curve x=n. Both lines hit it. You can make a better start than that.
 
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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