In this paper, a two-dimensional integral boundary layer method developed in a recent work is applied to ice accretion computations. The method has already been validated in terms of boundary layer dynamic effects in another article. It is here validated for its ability to capture ice shapes, once the method is included in an icing suite. To be more specific, results using the new boundary layer method are compared against experimental ice shapes and simulated ones with the widely-used simplified integral method. The validation is carried out at an aggregated level because icing databases generally provide access to final ice shapes only. But since the simplified integral method is used in many icing numerical tools, this comparison makes it possible to investigate the benefits of introducing the new method for calculating the boundary layer. The main outcome of the new method is an improvement of the prediction of the boundary layer prediction under smooth-wall assumption, which in turn improves ice shape prediction. It is shown that, overall, the ice shapes are indeed either better predicted with the new method than with the baseline approach, or equally predicted with both methods. In addition, since the heat transfer coefficient tends to be underestimated by simplified integral methods, the new approach tends to predict lower horn angles than the baseline approach. Finally, the consequences of these results on current and future developments of ice accretion solvers are discussed. In particular, the new method is better suited to a 3D extension than the simplified integral method.