Question

Alright, now dealing with Surface Integral problems. Posting below momentarily.

Answer 1

need help?

Answer 2

Yeah, just one moment.

Answer 3

G(x,y,z)=x, over the parabolic cylinder y = x^2, 0 leq x leq 2, 0 leq z leq 3

Answer 4

Alright, so I need to integrate the given function over the given surface. This is the first time I'm ever doing one of these problems, so it might be super easy, I just haven't tried yet until now; just posting it *immediately* in case I run into any misunderstandings, because I'm in a severe time crunch.

Answer 5

Alright, so G(x,y,z) is not defined parametrically, I need to get it into an either ecplicit, implicit, or parametrically defined form.

Answer 6

yeah um i dont get this sorry

Answer 7

But yeah, reading, not yet sure how to advance/proceed from here.

Answer 8

how do you find the surface area using integration?

Answer 9

Sort of learning/relearing how to do so, in better detail; Right now it looks like I have to take the magnitude of the cross product of two vectors to get something like a surface area differential?

Answer 10

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

Answer 11

yeah .. but that is after you parametrize the surface. There are couple of ways to do it.

Answer 12

First thing is to find the region of integration on xy plane.

Answer 13

Alright, is this like the shadow method, or what are you talking about, exactly? My book has doing the vector cross product part first in its examples.

Answer 14

look at the second and third method.

Answer 15

that is more easier than you currently doing .. if you want to do it first way, write the parametric equation of paraboloic cylinder.

Answer 16

My book chooses to treat a problem with a near identical setup as my current problem as case 1 and solve it that way. Alright, then.

Answer 17

@experimentX cam u help em

Answer 18

He is, joejoe.

Answer 19

huh

Answer 20

do you want to do it via parametric surface?

Answer 21

Yeah, to at the very least figure out/familiarize myself with the technique used in the first example. I'm getting how they took the cross product and stuff and how everything worked out, but confused about how to setup a parallel for this problem.

Answer 22

(?)

Answer 23

Alright, so parametrically defining a parabolic cylinder...I'm not sure how I should do that in this context, I could throw random tries at it, which gives me something like \[r = x, \ x^2 \ ,z\]

Answer 24

do you know about parametric equations?

Answer 25

@satellite73

Answer 26

Any suggestions or anything? I'm not sure how to move forward with this yet.

Answer 27

Alright, then..
\[r =r(u,v)=ui+u^2j+vk\]

Answer 28

\[(u,v): [0,2], \ [0,3]\]

Answer 29

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

Answer 30

can you imagine your surface .. or just draw rough picture of your surface?

Answer 31

Cross product between the two vectors gives you\[2u\ i-j \ ?\]

Answer 32

I dunno, I'm just going to keep doing what I'm doing, because I need to move fast on this, and doing what I'm doing seems to be getting closer to the answer quicker.

Answer 33

\[G(x,y,z)=x; \ \ \ G(r(u,v))=u\]

Answer 34

http://i.imgur.com/r7YOOpM.png

Answer 35

http://i.imgur.com/wp7Ez8L.png

Answer 36

you don't need vector integral .. you only need the scalar surface integral.

Answer 37

first thing you should do on multivariable calculus is ... visualize your equation in

Answer 38

Nope, apparently got it terribly wrong, but really want to get this problem done using *this* technique. My bounds of integration were correct, but my integrand was off.

Answer 39

I have no idea what your second to last post meant for me/how it alters the problem, can you point towards exactly what I did wrong? I need to figure out where that was.

Answer 40

your surface is \( y = x^2 \) , \(0 \leq x \leq 2, 0 \leq z \leq 3 \)

Answer 41

this is how your surface looks like