Is This Solution for a Calculus Problem Correct?

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Hey Guys, this is one of the Q's in my book which I have completed but would just like to check whether (a) it is correct and B whether I can leave it in this format for the answer?

cheers

I used the fundamental theorem part 1 and the chain rule due to upper limit of integration being x^3. I posted as attachements as my text wouldn't work in here.thanks heaps!

rhys
 

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I can't see your picture unfortunately.
 
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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