1. The problem statement, all variables and given/known data This comes from Mathematical Methods for the Physicist from Susan Lea, Chapter 1 Question 25 Part B (Incase anyone is familar with the book). The question asks to evaluate the line integral integral (u*dl) where the vector u is: u = x*y^2 i + y*x^2 j along the path of a semi-circle in the xy plane with a radius of a and the flat side of the semi-circle along the x-axis 2. Relevant equations see below 3. The attempt at a solution I am near certain the answer is 0, evaluating this in polar coor. gives me 0 and taking advantage of the del operator to find the surface integral gives me 0, so two methods out of three give me zero. however when I evaluate the integral in cartesian cord. I end up with 1/4 * a^4 for the half circle path and 0 for the bottom path. I am almost sure that the bottom path should not be zero for this to work, but I have no idea how to find it. My sanity really depends on knowing how I messed this up, because it looks so good on my paper :) Anyways, thanks for the help PS. Anyone know a good way I can enter equations onto the forums, I don't think typing it this way really makes the situation clear.