Did you use \(\displaystyle \oint_{C}\left[\left(\frac{-1}{\sqrt[3]{y}}\right)dx+\left(\frac{1}{\sqrt[3]{x}}\right)dy\right]=3a^{\frac{2}{3}}\int_{0}^{2\pi}\int_{0}^{a}dydx\) ?.
Where \(\displaystyle x=a\cdot cos^{3}(t), \;\ y=a\cdot sin^{3}(t)\)
This is using Green's Theorem. One can achieve the same result.
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