Question

@ganeshie8 , trying to deal with a Surface Integral. I'm not sure what I'm doing wrong here, posted below momentarily.

Answer 1

Part of it, near the end; reposting the rest of it in a second. http://i.imgur.com/5nUli9o.png

Answer 2

\[G(x,y,z)=x; \]Integrated over the surface \[y = x^2, \ \ \ 0 \leq x \leq 2, \ \ \ 0 \leq z \leq 3\]

Answer 3

I parametrized the surface as such: \[u = x, \ \ \ v = z; \ \ \ r(u,v) = u, u^2, v\]

Answer 4

\[r_{u},r_{v}=(1,2u,0), \ \ \ (0,0,1)\]

Answer 5

Cross product of the two vectors yields \[2u \ i - j\]

Answer 6

Alright, one sec, lol, forgot what I did after this. One moment.

Answer 7

Oh yeah, parametrized the vector field, \[G(x,y,z)=G(r(u,v))=u\]

Answer 8

Dot product between the two vectors

Answer 9

(Sorry, was posting on another thread, back)

Answer 10

Dot product just yields 2u^2?

Answer 11

why not simply use the formula
\[ \hat{n}dS = \langle -f_x, 1, -f_z\rangle dxdz\]

?

Answer 12

This is the book answer, have no freaking clue how they got there while I got somewhere very far away: http://i.imgur.com/soIJgWi.png

Answer 13

I don't know what that formula is, the formulae I'm supposed to be using are http://i.imgur.com/CbQYLfw.png

I'm trying to use the first formula

Answer 14

But yeah, I have no idea what the formula is/where that came from, what you're using, I'm just trying to use the first formula in that picture to solve the problem, and I'm not sure what I'm doing wrong with it.

Answer 15

GOT IT, I think

Answer 16

I think your textbook is using the last formula

Answer 17

just change the area element to `dxdz`

Answer 18

\[\iint_R G(x,f(x,z),z )~ \sqrt{f_x^2+f_z^2+1} ~dxdz\]

Answer 19

http://i.imgur.com/8zP4eE4.png

Answer 20

Then just evaluating it

Answer 21

http://i.imgur.com/Q0UHErN.png

Answer 22

I got there using the first one

Answer 23

http://i.imgur.com/Q0UHErN.png

http://i.imgur.com/xuHgdON.png

Answer 24

Alright, since I figured this one out, I'm going to take a shot at another problem using a different technique, or altogether a different problem. I'm running out of time.

Answer 25

Man, all of my messages are getting jumbled up, OpenStudy isn't playing well today

Answer 26

But yeah, I figured it out using that technique, going to move on to a different problem for now since I'm short on time.