The discussion focuses on finding the center of mass of region D in the (x, y) plane, defined by the lines y=x, y=4x, and the hyperbolas xy=1 and xy=9. Participants clarify that this is actually a centroid problem rather than a center of mass problem due to the absence of a density function. The correct approach involves using the center of mass formula with constant density, and the need to compute the area of the bounded region before proceeding with integration is emphasized.
PREREQUISITESStudents studying calculus, particularly those focusing on geometry and integration, as well as educators looking to clarify the distinction between centroid and center of mass problems.
HallsofIvy said:What have you done? The problem is to find a center of mass- why should there be a "?" on "use the center of mass formula"? Of course you shold use it. I can't speak toward "use the change of variables" because you haven't said what the integral is!
(Strictly speaking, this is NOT a "center of mass" problem at all because you have not given any density function so there is no "mass" and no "center of mass". It is a purely geometric "centroid" problem but that can be done exactly like a "center of mass" problem assuming constant density.)