# Line integral

Can line integral of a vector field ever be zero? If can, what is the interpretation of this value (0) ?

Thanks.

That's a very peculiar question. One of the first things students learn about path integrals is that if a f(x,y)dx+ g(x,y)dy is an "exact differential" (There exist a function F(x,y) such that $\partial F/\partial x= f(x)$ and $\partial F/\partial y= g(x,y)$ then the integral around any closed path is 0. And, since you refer to "vector fields", we can think of that as the integral of the vector field $f(x,y)\vec{i}+ g(x,y)\vec{j}$ over the path.