This study aims at exploring the role of argumentation in the process of shared meaning making that occurs between students as they use digital tools to explore the concept of the indefinite integral. The study followed 11 pairs of 17-year-old students as they worked together to solve the Indefinite Integral Task with the aid of a digital tool. The study was guided by the phenomenology perspective, which considers meaning making in mathematics as a progressive disclosure of the mathematical objects at stake. The data analysis tracked and categorized the components of students' argumentation as they progress in the meaning-making process of the indefinite integral. Our research findings revealed that the digital tool allows the students to produce evidence with which to substantiate and justify their arguments, and we also found that their frequent use of statements that built upon one another's arguments fostered the transition between one layer of disclosure and the next one.