I am trying to use the Fundamental Theorem of Line integrals to solve this problem. Basically, my problem is to find out if the following function is a gradient function:

H= -yi+ xj

I tried integrating both terms, but I cant seem to find any function where the gradient is equal toH. The path I am moving along is from the origin to (3,0), and then from there in a circle of radius 3 around the origin to the point (3/sqrt(2),3/sqrt(2)).

Could anyone help me here?