Additive tree functionals allow to represent the cost of many
divide-and-conquer algorithms. We give an invariance principle for such
tree functionals for the Catalan model (random tree uniformly
distributed among the full binary ordered trees with given number of
internal nodes) and for simply generated trees (including random tree
uniformly distributed among the ordered trees with given number of
nodes). In the Catalan model, this relies on the natural embedding of
binary trees into the Brownian excursion and then on elementary second
moment computations. We recover results first given by Fill and Kapur
(2004) and then by Fill and Janson (2009). In the simply generated case,
this relies on the convergence of conditioned Galton-Watson towards
stable Lévy trees. We recover results first given by Janson (2003 and
2016) in the quadratic case and give a generalization to the stable
case.