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.

As remarked by others, it is a typo. The correct formula is
$${\rm area}(S)=2\pi\int_0^l\ x(s)\ ds\ .$$
Intuitively one can interpret this formula as follows: The surface $S$ is a union of "infinitesimal lamp shades" of radius $x(s)$ and width $ds$. The surface of such an "infinitesimal lamp shade" is the same as the surface of a plane circular annulus of radius $x(s)$ and width $ds$, namely $2\pi\ x(s)\ ds$.
