Centroid

[bdcook22]

Is there a way to calculate the centroid for any given function. Say a region bounded by z=4-(x^2)-(y^2) and below the xy plane.

[DifEqRules]

If the centroid is the center of mass of an object with uniform density (I think it is, but am not sure), you can use these formulas

m = double integral over region of 1
mx = double integral over region of y
my = double integral over region of x

(my/m, mx/m) is centroid.

In your example, the integration would be easier if you switch to polar coordinates.