1. The problem statement, all variables and given/known data Find the circulation (line integral) of y2dx+x2dy for the boundary of a triangular region contained within x+y=1, x=0, and y=0. 2. Relevant equations Green's theorem 3. The attempt at a solution I think I actually already got the solution; I used the Green's theorem to get the curl of 2x-2y and integrated that for x from 0 to 1-y and y from 0 to 1 to get an answer of 0. However, I was a bit confused as I was trying to verify the solution by calculating the line integrals of each segment of the triangular region; I keep getting a different answer. I know that along the two axes, x/dx and y/dy are 0, respectively, so the line integrals of those would be 0, making the line x+y=1 the only contributor to the total integral. I parametrized y as 1-t and x as t, and integrated [(1-x)^2+x^2]*sqrt(2) from 1 to 0 of t; however, the answer to that is not 0. Why am I getting different answers here? Help would be appreciated.