(a) Write the definition of the surface integral of a scalar function f over a surface S.
(b) How do you evaluate such an integral if S is a parametric surface given by a vector function r(u, v)?
(c) What if S is given by an equation z = g(x, y)?
(d) If a thin sheet has the shape of a surface S, and the density at (x, y, z) is p(x, y, z), write expressions for the mass and center of mass of the sheet.