Finding the length of the curve

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find the curve at the point (-8,1) that gives the integrals length in the picture posted

i literally have no clue what to do. am i supposed to take the derivative of 16/y^3 and square it?
 

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billsauce said:
find the curve at the point (-8,1) that gives the integrals length in the picture posted

i literally have no clue what to do. am i supposed to take the derivative of 16/y^3 and square it?

Well, no. The 16/y^3 should be (x')^2 for one of those functions. Which one is it?
 
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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