Subtract 7xy (x² - 2xy + 3y²) -8x (x²y - 4xy + 7x y2) from3y(4x²y-5xy +8xy²)
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Not much can be done without knowing what 
is, but at the least we can set up the integral.
First parameterize the pieces of the contour:
where
and 
. You have
and so the work is given by the integral
First parameterize the pieces of the contour:
where
and so the work is given by the integral