I am currently learning about how to calculate moments of inertia of various shapes. I can calculate them fine using the Parallel Axis Theorem, but I am having some difficulty trying to understand the overall concept. Can somebody give me some practical applications of MOEs? I am also having some difficulty relating them to my understanding of integrals. I use no integration in my present calculations, since most of the shapes I am evaluating are composites of rectangles, triangles, circles, etc.. Would integration make even these simple shapes easier to calculate?