Question

What's the flux of the vector field F(x,y,z) = (e^-y) i - (y) j + (x sinz) k across σ with outward orientation where σ is the portion of the elliptic cylinder r(u,v) = (2cos v) i + (sin v) j + (u) k with 0 ≤ u ≤ 5, 0 ≤ v ≤ 2pi.

Answer 1

nice try bob

Answer 2

you're not that smart

Answer 3

Which is why I'm posting this.

._.

Answer 4

is this your question? or one you got from google?

Answer 5

pm me i have the answer

Answer 6

https://tex.z-dn.net/?f=%5Cdisplaystyle5%5Cint_0%5E%7B2%5Cpi%7D%281-%5Ccos2v%29%5C%2C%5Cmathrm+dv%3D5%5Cleft%28v-%5Cdfrac12%5Csin2v%5Cright%29%5Cbigg%7C_%7Bv%3D0%7D%5E%7Bv%3D2%5Cpi%7D%3D10%5Cpi

Answer 7

You can use the Divergence Theorem for this.

Start with \(div ~ \mathbf F = 0 -1 + x \cos z = x \cos z -1 \)

So you get:

\(\Phi = \int_A \mathbf F \cdot d \mathbf A = \int_V div \mathbf F ~ dV\)

\(\implies \int_V x cos z - 1 ~ dV = \int_V x cos z - 1 ~ dx ~dy ~ dz\)

Then make some sensible subs and get the Jacobian right.

Haven't done it myself, or had a look at the flux at the end caps, but it all tends to work out Ok on these type of questions.

Quite nasty though.

Answer 8

Just realised that the flux through the end caps is zero so you can use a surface integral as well

for the bottom end cap, \(\hat n = <0,0,-1> \) and z = 0 so \(\hat n \cdot \mathbf F = 0\)

for the top cap \(\hat n = <0,0,1> \), z = 5 so \(\hat n \cdot \mathbf F = x sin 5\). With symmetry, positive and negative x-values cancel to give zero flux there too.

still think you need to sort out that elliptical cylinder though with a substutition

Answer 9

If you're question is answered, please close it. Thank you.

Answer 10

I don't understand that language @Elsa213

Answer 11

not to mention your second word was a grammatical error

Answer 12

your*

Answer 13

better

Answer 14

Sorry cx
What do you not understand?

Answer 15

yer layngwidge eez yewsholly theeez

Answer 16

Ef yewr question es answered, pl0x close et. Tenk yew.

Answer 17

That's better? e.e

Answer 18

yeee

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Answer 19

peeeple wer mad and repurting mee

Answer 20

Deed yew keel em?

Answer 21

yeees

Answer 22

Congratulationss, boi