If you mean that little 'r' is a variable radius then you must integrate (option 1), because the charge density is a function of the radius.
Integrate over a volume if the problem is 3dimensional, or over an area if the problem is 2d.
A computer model has found geometries and frequencies associated with various vibration modes of my cantilever (see pictures). The model only accounts for an anchor at the far end and material properties of each layer.
In reality the bottom layer is piezoelectric, it is glued to the glass top...