Question

whats the flux? vector field=xi+2zj+yk; S that portion s is part of the cylinder y^ 2 +z^2=4 in the first octant bounded by x =0,x=3,y=0,z=0(assuming surface S is oriented upward)

Answer 1

Really? It's been staring you in the face, @dan815 :D
\[\huge (x,y,z)\rightarrow(r,\theta, z)\]
\[\huge r=\sqrt{x^2+y^2}\]\[\huge \cos(\theta)=\frac{x}r\]\[\huge\sin(\theta)=\frac{y}r\]
\[\huge z=z\]

Answer 2

what is that?

Answer 3

Converting from xyz to cylindrical.

Answer 4

i dont get it T_T

Answer 5

so how do i reprsent my cylinder if its like this

Answer 6

Nice drawing ^.^
You must understand, I've never heard of flux before :)

Answer 7

u dont need to know that just tell me how i parametrize this cylindrical coords

Answer 8

^I don't know what that means...
Maybe I'm not the best person for this question :)

Answer 9

Use the parameterization r(u, v) = <u, 2 cos v, 2 sin v> for u in [0, 3], and v in [0, π/2].

Answer 10

thats what i found on the internet does that make sense to you?

Answer 11

Nope :)
What I found is the Gauss-Divergence Theorem. ^.^

Answer 12

yaa this is like that

Answer 13

Well, why don't you just use that? I really hate integrals with circles through them...

Answer 14

@wio your assistance needed plz

Answer 15

If we could just use Gauss' Divergence, it just becomes equal to
\[\huge \iiint\limits_V (\nabla \cdot \vec{F})dV\]

Answer 16

well that comes in chapter 9.15 i am still on 9.13 so it wants me to use this method right now

Answer 17

What year are you in, @dan815 ?

Answer 18

2

Answer 19

We need someone that specialises in this sort of evil Integral madness.. definitely not me...
I was just using Google earlier :)

Answer 20

wio is like a professor

Answer 21

lol

Answer 22

Well, there are like 4 surfaces here, right?

Answer 23

he always anwers these kind of questiosn for me

Answer 24

If we can't do divergence theorem then we are going to do a ton more work.

Answer 25

i think this is what i need to find

Answer 26

You need help parametrizing the surfaces?