Chapter 15.R, Problem 60E

(a) Evaluate ${\displaystyle \underset{D}{\iint }\frac{1}{{\left(x^2+y^2\right)}^{n/2}}dA}$, where n is an integer and D is the region bounded by the circles with center the origin and radii r and R, $0<r<R.$

(b) For what values of n does the integral in part (a) have a limit as $r\to 0^{+}$?

(c) Find ${\displaystyle \underset{E}{\iiint }\frac{1}{{\left(x^2+y^2+z^2\right)}^{n/2}}dV}$, where E is the region bounded by the spheres with center the origin and radii r and R, $0<r<R$.

(d) For what values of n does the integral in part (c) have a limit as $r\to 0^{+}$?