Calculating line integrals.... Ok, the problem is: h(x,y) = 3x (x^2 + y^4)^1/2 i + 6y^3 (x^2 + y^4)^1/2 j; over the arc: y = -(1 - x^2)^1/2 from (-1,0) to (1,0). In my notes, I had written: if h is a gradient, then the INTEGRAL of g*dr over curve C depends only on the endpoints. Also, if the curve C is closed AND h is a gradient, then the integral of g*dr over curve c is 0. So, my question is, when testing to see if a given function like the one above, should you just test to see if: partial derivative of the i component with respect to y EQUALS the partial derivative of the j component with respect to x? If not equal, then it is not a gradient, right? Thanks.