Update

Signed-off-by: Marcello Seri <[email protected]>

7-integration.tex

@@ -372,7 +372,7 @@ \section{Integrals on manifolds}
 Armed with our experience with line integrals, fond memories of multivariable analysis and our recent discoveries, we are finally ready to talk about integrals.
 Let's keep things simple and go one step at a time.
 
-% TODO: properly explain how the change of variable in Euclidean space requires the absolute value of the Jacobian determinant, and thus in our definition we need to take into account the orientation and compensate with a minus sign if necessary.
+% TODO: properly explain how the change of variable in Euclidean space requires the absolute value of the Jacobian determinant while the transformation of a k-form only involves the determinant itself, and thus in our definition we need to take into account the orientation and compensate with a minus sign if necessary.
 
 \begin{definition}\label{def:intnform:chart}
   Let $M$ be a smooth $n$-manifold and $(U,\varphi)$ be a chart from an oriented atlas of $M$ with coordinates $(x^i)$.