Suppose (x, y) is continuous and nonnegative over a region R in the plane with a defined

Suppose ƒ(x, y) is continuous and nonnegative over a region R in the plane with a defined area A(R). If ∫∫_R ƒ(x, y) dA = 0, prove that ƒ(x, y) = 0 at every point (x, y) ε R.