Mean value theorem for integration

NIZBIT
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The problem states:

Find all values of c such that \sqrt(1+\sqrt(x)) satisfies the statement of the mean value theorem for integration on the interval [0. 1]. Also express the result in exact form completely simplified.

I am a little confused. I'm just finding the definite inegral? I don't understand the second part to the equation.
 
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Do you know what the mean value theorem for integration is? If not, try looking it up.
 
Well that clears it up! Thanks!
 
No problem!
 

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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