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**keysar7** a) Parametrize the curve $\displaystyle x^{\frac{2}{3}}+y^{\tfrac{2}{3}}=a^{\tfrac{2}{3}}\ \$ in the standard counterclockwise sense.

b) Evaluate $\displaystyle \text{F(x) = (}\tfrac{-1}{\sqrt[{3}]{{y}}}\text{ ,}\tfrac{1}{\sqrt[{3}]{{x}}}\text{ )} $ over one complete transversal of the above curve.

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My approach & Answer:

a)

$\displaystyle x=a\text{ }\cos ^{3}t$

$\displaystyle y=a\text{ }\sin ^{3}t$

$\displaystyle 0\text{ }\leq t\leq \text{ }2\pi $

b) Since the field is not conservative, we have to find the line integral (i.e. the answer is not zero)... My final answer is $\displaystyle -6\pi a^{\tfrac{2}{3}}$

However, I think the negative sign is not correct because the force field is along the path of motion, meaning positive would make more sense...

What do you think?