Find the length of the given curve $\displaystyle x=3y^{\frac{4}{3}}-\frac{3y^{\frac{2}{3}}}{32} $
where the bounds are given by $-8 \leq y \leq 343$.
I can solve for the positive part (0 to 343), but I am unsure of how I would go about integrating $\int_{-8}^{0} \sqrt{1+\left(\frac{dx}{dy}\right)^2}dy$
Thanks again for any help!