path independence

Let F1, F2, and F3 be functions of (x, y, z). Suppose that for every given pair of points A and B in space, the line integral ∫(F₁dx+ F₂dy + F₃dz) evaluates to the same value along...

Consider points $$P$$ and $$Q$$ in $$xy-$$plane with $$P=(1,0)$$ and $$Q=(0,1).$$ The line integral $$2\int\limits_P^Q {\left( {x\,dx + y\,dy} \right)\,\,} $$ along the semicircle...