Calculus II - Centroid (Center of Mass) of a Planar Region: Worked-Out Examples

MATH 1112 Calculus II
Class 21 - Video 2
We take the integration formulas for finding the centroid of a planar region (that we derived in a previous video) and apply them to several examples: rectangle, triangle, semicircle, parabola. We demonstrate how to use the formulas, and give some advice for applying them to examples. Along the way, we emphasize some physical intuition; in particular, we see how some of the examples match what we would expect from the physics of real life, so to speak. Finally, we state a generalization of the formulas for a planar region bounded between two curves, and we show the solutions for that example so the viewer can check their work.