AP Annual Conference Submission
Change at one point is the central idea on which the differential, and thereby calculus, is built. The differential allows us to find the derivative (the rate of change at one point). It is used in finding exact area under a curve (using rectangles with one point width) and volume (by using shapes with one point dimension). The Advanced Placement exam will test on areas and volume; both will require making cuts “dx” thick. Participants will be able to lead their students in a directed discussion that will facilitate the understanding of how the integral is used. Each time an integral is set up certain details must be addressed. Whether finding area, volume, arclength or anything else the same questions can be asked to help teachers and students alike build their integral correctly. This lesson will demonstrate once you know how an integral works, the context of the example will not change the way the integral is set up.