Mathematically, we divide an area into infinitely small rectangles, and the area of each rectangle is called infinitesimal ds. For the three-dimensional smooth surface S, there are: ∫∫ SDS = ∫∫ D _ xy √ {1+(f _ x') 2+(f _ y') 2} dxdy, where d _ xy is the projection of S on the xy plane. Here, f _ x' and f _ y' represent the partial derivatives of the function f to x and y respectively. So the infinitesimal area ds is equal to (1+(f _ x')2+(f _ y')2)dxdy.