In the next problem you must use and explain in detail how do you use the Stoke's Theorem to get to the answer. It should also include an analysis on the orientation of the surface and its boundary.
Find the work done by the vector field $F(x,y,z)=(-y,x,0)$ when displacing a particle on the boundary of the surface parameterized by $p(r,\theta)=(r(2+cos \theta)cos\theta, r(2+cos \theta)sin \theta, sin \theta)$ where $0 \leq r<1,0<\theta<2\pi$.
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Bounty seems too low.
The range of theta looks suspicious too, it probably goes from 0 to 2pi.
very suspicious. also, p(.) has only 2 components, how's that a surface in R^3?
Please double check the statement of your question. There seems to be typoes.
Ok, I changed it.
There is still a typo on the first component of p(r,theta)