Hi, I would appreciate if someone could help. thanks.

Calculate the work done by the non conservattive force F=x³j in moving a particle,around the regular hexagon with vertices at (√3,1),(0,2),(-√3,1),(-√3,-1),(0,-2) and (√3,-1) in that order. (use greens theorem).

For this question I tried to use symmetry : I sketched the hexagon out then,I divided into half.

y-y1=m(x-x1)

and the formula m(gradient)=(y2-y1)/(x2-x1)

Please see diagram attached : Attachment 28760

For C1:

y=(x²+2x√3+6)/3For c2:y=2+(x/√3);For c3:y=1

I am really not sure what I am doing wrong . could someone please check. obviously if its a positive gradient ,need pos sign for neg gradient slanting the other way I need a negative sign . is there anything else I have to account for ?cuz I seem to be somethimes getting wrong answers off by minus 1.