Discovering Integration Through a Physical Phenomenon

Abstract This article outlines a method of conducting a laboratory designed to discover mathematical integration with students. The results are produced and verified in the laboratory by students. Understanding that an integral is defined by the area bounded by a function of x and the x-axis from a point a to a point b is challenging. Students often have trouble connecting this idea to any physical phenomena. While classroom exercises tend to show the mathematical mechanics of integration, few exercises demonstrate the process of more abstract integrals. Our in-class activity allows for hands-on integration of any function. The students physically integrate power as a function of distance as light passes through a function cut-out. Students can actually collect data and see the integral come to life. We restrict how much light passes through the cut-out using a razor blade and we record the power of this light as the razor blade is translated; thus the data collected are the integral of the cut-out shape....