From O to A we have that y does not change so dy = 0.Evaluate the line integral where C comprises the three sides of a triangle joining O (0, 0) A (2, 0) and B (0, 2)
From A to B the path is the line from (2, 0) to (0, 2). This is a segment of the line y = -x + 2 as x goes from 2 to 0, so
So the overall integral will be:
So from B (0, 2) to O (0, 0) dx = 0, with x = 0. Thus
So my final integral is STILL .
And if you look at the succession of points I did the integral in the counterclockwise sense. I can't argue with your result (though I was never very good at implementing Green's theorem anyway) but I can't find a mistake in my own work?