As you can imagine, the smaller you make the area segments, the closer this gets to the true mass, since your approximation of constant sigma is more accurate for smaller segments. If you let the segment area dA approach zero and N approach infinity, the summation becomes integration, and you have Mass = \(\int_{S}\sigma(x, y)dA\) : This is the area integral of the scalar function sigma(x, y) over the surface S.