AP Annual Conference Submission
Definite integrals can be interpreted as accumulated rates of change of functions and as limits of Riemann sums of functions. The former interpretation has been useful for students taking recent AP Exams. The latter is more generally applicable, particularly if it is not clear to the student that the given function is the rate of change of the desired quantity. For example, cross-sectional area of a solid is the rate of change of volume, force exerted on an object is the rate of change of work done in moving the object, and density of an object is the rate of change of its mass. Students comfortable with the Riemann sum interpretation could work problems like the plankton problem, BC-2 on the 2018 exam, that caused other students so much difficulty. In this session participants will learn strategies to convey to students the concept of definite integral in the first week of calculus, leading to later proof of the FTC, and how to choose which interpretation to apply in a given problem.