In this Calculus 2/Calculus BC project, students use the formulas from class to actually calculate the centroid (balancing point) of a uniform density object.
Students first trace a banana on graph paper, then find actual regression lines, the calculate the centroid.
Trial and error will lead students to correcting mistakes and a deeper understanding of limits of integration, regression lines, and the formulas for area between two curves and the x and y coordinates of a centroid. This fostered discussions in my class as well as had students doing "extra" work on their own to get better approximations.
Grading is easy and pay off is huge! Students love seeing something theoretical "actually work"!