Investigating Interpretations of Integration: Students’ Multiple Manifestations of dx

Integrals can be conceptualized with an infinitesimal or a limit definition, and holding a certain conceptualization may change how someone frames and solves an integral problem. We asked second-semester calculus-based Intro Physics students questions involving integrals and derivatives in physics and math contexts. We focus on one atypical integral question from our semi-structured think-aloud interview in which students had differing answers and comments. Student work and utterances led us to define two conceptual resources concerning infinitesimals, which correspond to the different definitions of integration. This work highlights subtle differences in students' interpretation of integration and areas for future study.