Mathematics · Vector Calculus

Given below are two statements: Statement I: If φ(x, y), ψ(x, y), &partial;φ&partial;y, and &partial;ψ&partial;x are continuous functions over a region R bounded by a simple closed curve C in the xy-plane, then ∮C (φ dx + ψ dy) = &iint;R (&partial;ψ&partial;x - &partial;φ&partial;y) dx dy. Statement II: If F̅ is a vector point function and V is the volume enclosed by a closed surface S, then the total flux of F̅ through S is given by the volume integral ∭V F̅ dV. In the light of the above statements, choose the most appropriate answer from the options given below: