Papuss's Theorem for Surface Areas

Larrytsai
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y=sqrt(2x+1), 0≤x≤2

Find the area of the surface by using the second theorem of Pappus.

S= 2pie(row)L

I cannot find what the centroid is, i have length as 2
 
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Find the area of what surface? A graph in the xy plane is not a surface. And your arc length isn't correct.
 
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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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