Calculate the area of the surface given by $$ x^2+y^2 = 2x $$ and delimited by the cone of equation $$ z^2 = x^2 + y^2 $$ My problem is that I can't see how can the first equation represent a surface (ok, I know that it is, but how can I express it in a more natural form as a two varible function or in a parametric way, e.g. $f = f(x,y)$, or $\psi(u, v) = (x(u,v), y(u,v), z(u,v))$), and therefore I can't solve this problem.
Any ideas how to solve it? Or some useful explanation?
My problem is that I don't know how to set up the integrals for the area of the surface... How to consider the fact that the "empty cylinder" is limited by the cone?