section_path: Area formulas/General formulas/General formula for surface area
section_name: General formula for surface area
paragraph_text: General formula for surface area
  
  The general formula for the surface area of the graph of a continuously differentiable function z = f (x, y), {\displaystyle z=f(x,y),} where (x, y) ∈ D ⊂ R 2 {\displaystyle (x,y)\in D\subset \mathbb {R} ^{2}} and D {\displaystyle D} is a region in the xy-plane with the smooth boundary:
  
  An even more general formula for the area of the graph of a parametric surface in the vector form r = r (u, v), {\displaystyle \mathbf {r} =\mathbf {r} (u,v),} where r {\displaystyle \mathbf {r} } is a continuously differentiable vector function of (u, v) ∈ D ⊂ R 2 {\displaystyle (u,v)\in D\subset \mathbb {R} ^{2}} is: