Question-

Let C be a differentiable curve contained in the portion 0 inferior or equal to x inferior or equal to 1 of the first quadrant, starting on the positive y-axis and ending somewhere on the line x=1.

Show that the flux of the vector field F

F=(2xy-2x^4*y)i+(4x+4x^3y^2-y^2)j

Across C is always equal to -2.

Hint: Apply Green Theorem to the region between C and the x-axis.