There are several improper integrals which keeps puzzling me. Let's talk about them in xoy plane. For simplicity purpose, I need to define r=sqrt(x^2+y^2). The integrals are ∫∫(1/r)dxdy, ∫∫(x/r^2)dxdy, ∫∫(x^2/r^4)dxdy, and ∫∫(x^3/r^6)dxdy. Here ‘^’ is power symbol. The integration area D...