Calc. Help Please?

Let f = x(x+y) , g = xy^2
Then F = f i + g j
r = x i + y j
dr = dx i + dy j
Hence, ∮ c F．dr = ∮ c ( fdx + gdy )

∮ c F．dr
= ∮ c ( fdx + gdy )
= ∫ ∫ R ( ∂g/∂x - ∂f/∂y )dxdy , by the Green's Theorem
= ∫ [0,4] ∫ [y=0,y=x] ( y^2 - x ) dy dx
= ∫ [0,4] { [ (1/3)y^3 - xy ] , from y=0 to y=x } dx
= ∫ [0,4] [ (1/3)x^3 - x^2 ] dx
= [ (1/12)x^4 - (1/3)x^3 ] , from x=0 to x=4
= (1/12)4^4 - (1/3)4^3
= 0 ..... Ans