I did the following(for the first problem):
I imagined cylinder ,
First I consider the pipe without top and bottom ( and )
Since for , has components 1 and 1. The integral for pipe will be simply
Now I consider top and bottom discs: integral for bottom disc will be because it's at . The most interesting is top disc ( and ). For area of top disc I will have the following integral but the top z is 1 so integral is . dA is a little area at the top disc, and I think it is where So finally my integral is Taking it from 0 to 1 I get . So the finall result is:
I have to submit both problems very soon. Can you check if I did first correctly? How should I prove second one?