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Procedure. 1) Examine whether f (x) has a continuous extension F (x) to A. If this is the case, then f (x) dS = A F (x) dS, A where the right hand side is calculated by well-known methods, and the problem is solved. 2) If f (x) does not have a continuous extension to A, we continue by an analysis of the sign of f (x). This step is extremely important! Divide A into two subsets A+ = {(x, y) ∈ A | f (x, y) ≥ 0} and A− = {(x, y) ∈ A | f (x, y) ≤ 0}. e. the curves where f (x, y) = 0. These curves divide the domain into open sub-domains.

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