Caculating integral with binomial coefficient

cielo
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Homework Statement





Homework Equations


What is the integral of

\int^{0}_{1} nCy x^{y} (1-x)^{n-y} dx ?


The Attempt at a Solution


\left(nCy\right) \int^{0}_{1} x^{y} (1-x)^{n-y} dx
 
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It looks like a beta function to me.
 


Dick said:
It looks like a beta function to me.

Thank you for your good idea Dick! =)
 

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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