For this problem I started with part a by saying that the area diverges by using the p test where p=1. For the second half I found the area of a cross sectional washer to be pi(1 - (1/x^2))delta x. Taking the integral of this from to infinity would result in an infinitesimally large area - an infinitesimally small area, thus resulting in another divergence. Is this correct? Why should I have been surprised by the answer?