What is the Integral of Riemann's Sum with Square Roots?

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Homework Statement


Convert the Riemann's Sum to an integral:

(1/50) * [(sqrt(1/50)) + (sqrt(2/50)) + (sqrt(3/50)) ... + (sqrt(50/50))]


Homework Equations





The Attempt at a Solution



(1/50) times Integral (upper limit 1 and lower limit 0) of sqrt(x) dx
Is my solution correct?
 
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^There is no (1/50).
 
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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