Pappus's theorem Let $S$ be a surface of revolution in $\mathbb{R}^3$ (2-dimensional) and let $C$ be its generating curve. Let $s$ be its arc lenght. Let $x = x(s)$ be the distance from a point in the curve to the $Oz$ axis (C lies in the $xz$ plane and we rotate it around $Oz$).
In my DG book, it says that 
$Area(S) = 2x \int_0^l \pi(s) ds $. Where $l$ is the lenght of the curve. Although it says nowhere what this $\pi$ function is.
I've been able to prove, using the theory formulated in the book that
$Area(S) = 2\pi \int_0^l x(s) ds $ where this $\pi$ is the regular 3.14... $\pi$
The proof looks pretty correct to me. Is it safe to assume that the book was printed wrong?
thanks in advance.

Yes, it was typo. For the correct statement, you can look at p.101, Exercise 11 in Section 2-5 in the book "Differential Geometry of curves and surfaces" by Do Carmo.
