Find the centroid of the region

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Homework Statement


Find the centroid of the region bounded by ...

y=x^3, x+y=2, y=0

Homework Equations


The Attempt at a Solution



I think you find the area of the region which is 5/4
 
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Sure, that's the area alright. What else do you have to compute to find the centroid?
 


That is NOT what I get for the area! dohsan, could you show your work?
 

Thread 'Finding the nth roots of a complex number'

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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