I have a question which asked me to evalute the line integral around the curve x^2+y^2=r^2 (z=z0 (a constant)) of the following vectors: (0, z^2, 2yz) and (yz^2, yx^2, xyz) the first one I get as 0, and the second one I get as: -pi(r*z0)^2 Those answers I'm pretty sure are right The next part of the problem asks to find grad(yz^2) which I calculate to be: (0,z^2, 2yz). The problem then asks to use this result to explain the answers to the two line integrals in the first part of the question. Now the first integral is easy to explain...since it is the integral of the gradient of a scalar...hence a conservative field, hence the integral around a closed loop i.e. a circle, is 0! But I cant seem to explain the 2nd integral, any ideas anyone?