Because I can. An object exists on a plane, is bounded by the parametric equation x=cos(t)^3 y=sin(t)^3, and has a density at any point of d=(e^x)/(y+5)^2 (units of mass and length are irrelevant). Please find the center of mass.
First find x^2 and y^2 then add them to create a circle which has a radius of 1... then we need to calculate 3 double integrals, M, Mx and My. all of them will have both integrals' bounds from 0 to 2π, and also it doesn't matter if integrate x or y first (fubini), we will choose whichever is easier. For M: the function inside will just be d, and we integrate that twice. For Mx: the functio inside will be d*y For My: the function inside will be d*x The center of mass will have coordinates x=My/M and y=Mx/M I probably am wrong in the bounds of the integrals because I haven't really gotten into multivariable integrals and always mess up the bounds. Most times I put them randomly :P .
