Find Curve for max work of a Force field

[Engels]

Homework Statement

We have the force field F= (-4y+yx^2)i - (xy^2)j. Find the simple closed curve in which the work produced by the Force field is maximum

Homework Equations

vector calculus( curved intergrals second type, green stoke's gauss theorems...)

 

[gabbagabbahey]

What's the definition of work (it involves an integral)? How would you go about maximizing some known function g(x,y)? Apply that to the definition of work, using the fundamental theorem of calculus.