The Accumulator Function

This activity is for a first-year Calculus course. It introduces the accumulator function, which will lead into the development of the Fundamental Theorem of Calculus. Students begin by evaluating a sequence of definite integrals using a geometric approach to the area. Each integral in the sequence only changes the upper limit. They then compare and contrast each expression, noting that the upper limit of integration is the only difference between them. This suggests that we can create a function (the accumulator function) that is dependent on the upper limit. After formalizing the language and notation, students continue with their analysis of this new kind of function and begin to see evidence of the relationship described by the Fundamental Theorem of Calculus. This activity corresponds to topic 6.4 of the AP Calculus AB/BC Course Description.

By Pablo Garcia