Method for finding the
potiential fuction f(x,y) given the gradient vector field F = < fx,
fy>:
1) Evaluate f(x,y) = S fx dx = g(x,y) + C1(y),
where C1(y) represents terms
not containing x.
2) Evaluate f(x,y) = S fy dy = h(x,y) + C2(x),
where C2(x) represents
terms not containing y.
3) f(x,y) = g(x,y) + (sum of terms in h(x,y) not
listed in g(x,y)) + K,
where K is a constant
Proof
of method: