Question

A force acting on a particle moving in the xy plane is given by Fx = (2yi +x^2j)N, where x and y are in meters. The particle moves from the origin to a final position having coordinates x=5.00m and y=5.00m, as in Fig. Calculate the work done by F along (a) OAC, (b) OBC, (c) OC.(d) Is F conservative or nonconservative? Explain.

Answer 1

If you tried to copy and paste, that does not work here. Therefore I do not know your paths.
If the force is conservative the curl of the force vector is zero and it can be describedas the gradient of a potential. assuming you mean F = 2y i +x^2 j

i j k
d/dx d/dy d/dz
2 y x^2 0

[d/dx(x^2) - d/dy(2y)] k = (2x-2)k
see http://www.wolframalpha.com/widget/widgetPopup.jsp?p=v&id=85afa8b72bd564fc6c84dde9f0393305&title=MathsPro101%20-%20%20Curl%20and%20Divergence%20of%20Vector%20Fields&theme=gray&i0=2y&i1=x%5E2&i2=0&i3=curl&podSelect=&includepodid=VectorAnalysisResult
so
not a conservative field and the work done will depend on the path taken

Answer 2

yes