Answer the following vector calculus problems. Be sure to solve all parts. Thank you!

3. (a) (20 pts) Consider the double iterated integral 1 1 1 dxd. [a]; 1933; y Since the integrand is unbounded on the rectangle R = [0,1] x [0,1], the double integral is dened as the limit of double integrals over the rectangle [0, t] x [0, t] as t } 1'. This is called an improper integral which is very similar to improper inte- gral for one-variable functionsln short, you can forget about it being unbounded. Evaluate the double iterated integral by using the change of variables uv ad n+1; n = . i ,, Remark: You may assume change of variables formula holds and that you can interchange the order of integration for improper integrals. Basically, treat it like any good old double integral. 3:: (b) (20 pts) Let BR be the ball centered at the origin with radius R, i.e . 33 = {(m,y,z) E R3 | 2:2 + y2 + 22 S R}. Let N = (0,0,3) be the North Pole and dN(a:, y, 2) be the distance from N to (:5, y, z) . Using multiple integrals, nd the average distance between points in 33 and N, that is, nd the average value of (in; over BR