We used student surveys to assess changes in proficiency with integral calculus, calculus self-efficacy, and physics self-efficacy in a second semester course of introductory physics focused on electricity and magnetism. In addition to tracking the fraction of quantitative problems solved correctly on the calculus proficiency survey, we also used principal component analysis and factor analysis of the data collected using all three surveys to evaluate changes in student proficiency and attitude. These analyses indicate that while all students demonstrated an increase in proficiency with integral calculus, including using integration in the context of physics, women displayed larger gains than men. Conversely, men showed larger gains in calculus self-efficacy. When combined, these data suggest that student identity modulates the correlation between a student's calculus abilities and their perception or self-evaluation of those abilities. We further show that calculus self-efficacy and physics self-efficacy are more strongly correlated for women than for men. These data suggest that student identity affects the coupling between calculus self-efficacy and physics self-efficacy, which could be consistent with previously published work demonstrating that mathematics self-efficacy is modulated by student identity [A. C. Frenzel et al., Learn. Instr. 17, 478 (2007); A. C. Frenzel et al., Eur. J. Psychol. Educ. 22, 497 (2007); R. A. Louis and J. M. Mistele, Int. J. Sci. Math. Educ. 10, 1163 (2012)]. These results may thus also highlight a potential contributing factor to gender-related differences in physics self-efficacy [J. M. Nissen and J. T. Shemwell, Phys. Rev. Phys. Educ. Res. 12, 020105 (2016); E. M. Marshman et al., Phys. Rev. Phys. Educ. Res. 14, 020123 (2018); T. Espinosa et al., Phys. Rev. Phys. Educ. Res. 15, 010132 (2019)] as well as the complexity of addressing those differences.