Bajracharya and Thompson on the Application and Understanding of the Fundamental Theorem of Calculus in Physics

R. R. Bajracharya and J. R. Thompson
Student application and understanding of the fundamental theorem of calculus at the mathematics-physics interface
Proceedings of the 17th Annual Conference on Research in Undergraduate Mathematics Education, pp. 43-54 (Mathematical Association of America, 2014).

We studied students’ understanding of the Fundamental Theorem of Calculus (FTC) in graphical representations that are relevant in physics contexts. Two versions of written surveys, one in mathematics and one in physics, were administered in multivariable calculus and introductory calculus-based physics classes, respectively. Individual interviews were conducted with students from the survey population. A series of FTC-based physics questions were asked during the interviews. The written and interview data have yielded evidence of several student difficulties in interpreting or applying the FTC to the problems given, including attempting to evaluate the antiderivative at individual points and using the slope rather than the area to determine the integral. The interview results further suggest that students often fail to make meaningful connections between individual elements of the FTC.