Thread: Length of Curves

Find the length of the curve

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It says it in the book that 1 + \left(\frac{dx}{dy}\right)^2 is a perfect square but I'm not seeing that. Any help?

Edit: I think I found my error. :|

The problem starts here

g'(y) = y^2 - 1/(4y^2)

g' (y) ^2 = y^4 -1/2 + 1/(16y^2)

1 + g' (y)^2 = y^4 +1/2 + 1/(16y^2) = [y^2 +1/(4y^2)]^2