Given a vector field, show flux across all paths is the same.

[megadong]

Homework Statement

Given the vector field F=3x^2i-y^3j, show that the flux over any two curves C1 and C2 going from the x to the y axes are the same.

Homework Equations

Flux = int(F dot n ds) = int(Mdy - Ndx)
divF = Ny + Mx

The Attempt at a Solution

We can show the divergence of the field is zero => Ny = -3y^2 and Mx = 3y^2
so divf = Ny + Mx = 0... does this help in any way? Thanks

 

[HallsofIvy]

Try using Green's theorem.