Question

Stokes' Theorem problem, posted below shortly.

Answer 1

Posting the prompt in an imgur link this time: http://i.imgur.com/yfzci0h.png

Answer 2

\[\int\limits_{}^{}\triangledown \times F \cdot n = \iint \text{(some stuff)}\]

Answer 3

No... \[
\int_C\mathbf F ~d\mathbf r = \iint_S\nabla\times\mathbf F~d\mathbf S
\]

Answer 4

you want to evaluate using stokes thm first ?

Answer 5

I was like 99% sure that Stokes' Theorem had grad cross f dot n in its argument. What am I thinking of that isn't Stokes' but also has that integrand?

Answer 6

And yeah, using stokes theorem would be good.

Answer 7

okay start by finding the curl : \(\nabla \times \vec{F} \)

Answer 8

\[\vec{F} = \langle x^2y,~ y,~ xz\rangle \]

Answer 9

Alright, doing that now. Need to remember how to write matrices in LaTeX again, lol...

Answer 10

Whatever, just going to compute it without writing up the matrix.

Answer 11

Or is not a closed interval? :o

Answer 12

(I don't know the LaTeX command for that kind of integral, heh, looking at it now)

Answer 13

Well, it's the boundary of a surface

Answer 14

Ah, got it.

Answer 15

So it will be closed path

Answer 16

Just learned Stokes like 3 days ago.

Answer 17

Yeah, I'm trying to remember everything that I've already repeatedly learned, I have about the long term memory retention of a poodle.

Answer 18

\[\text{Curl} \ F=-(z)j+(x^2)k\]

Answer 19

lets double check with wolfram
http://www.wolframalpha.com/input/?i=curl+%28x%5E2y%2C+y%2C+xz%29

Answer 20

Oh, yeah, I see why.

Answer 21

Alright, got that part. Man, I'm just out of willpower right now, this isn't even necessary tough, but I'm just burnt out from my previous three finals in the last ~36 hours. Somebody tell me to keep trying, lol.

Answer 22

this is fairly easy compared to your previous problem
find the ndS and take dot product