Please, help somehow if you can!

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- December 12th 2008, 02:15 PMandreas2 very difficult Calculus questions
Please, help somehow if you can!

- December 13th 2008, 04:33 AMandreas
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? - December 13th 2008, 07:14 PMmr fantastic
I don't think the integral of F over the curved surface of the pipe is equal to : If you parametrise the cylindrical surface then an infinitesimal element of the curved surface can be written as

.

Then the surface integral of F over the curved surface becomes

since on the curved surface. I get zero as the answer.

So I think the integral over the closed surface will actually be . Doing the calculation using the divergence theorem I get the same answer.