A community for students.
Here's the question you clicked on:
 0 viewing
 2 years ago
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.
 2 years ago
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.

This Question is Closed

kumar2006
 2 years ago
Best ResponseYou've already chosen the best response.1∫∫s F dS ... F = e^(y) i  y j + x sin(z) k s: the elliptic cylinder r(u,v) = 2 cos(v) i + sin(v) j + u k ... 0 ≤ u ≤ 5, 0 ≤ v ≤ 2π ∫∫s F dS = ∫∫∫v ∇·F dV ∇·F = x cos(z)  1 = ∫∫∫v x cos(z)  1 dx dy dz v: x² + 4y² ≤ 4 ; 0 ≤ z ≤ 5 let u = x , v = 2y , z = z ∂(u,v)/∂(x,y) = 2 = 1/2 ∫∫∫v u cos(z)  1 du dv dz v: u² + v² ≤ 4 ; 0 ≤ z ≤ 5 let u = r cos(θ) ; v = r sin(θ) ; z = z ∂(u,v)/∂(r,θ) = r = 1/2 ∫∫∫ (r cos(θ) cos(z)  1) r dr dθ dz {(r,θ,z)  0 ≤ r ≤ 2 ; 0 ≤ θ ≤ 2π ; 0 ≤ z ≤ 5} = 1/3 ∫∫ (4 cos(θ) cos(z)  3) dθ dz {(θ,z)  0 ≤ θ ≤ 2π ; 0 ≤ z ≤ 5} = 2π ∫ dz {(z)  0 ≤ z ≤ 5} = 10π

kumar2006
 2 years ago
Best ResponseYou've already chosen the best response.1∫c F·dr .... F = (x + y) i + (xy) j  (z^2) k ; c: from (0,0,0) to (1,3,1) to (2,1,4) → (0,0,0) to (1,3,1) x = t ; y = 3t ; z = t ; 0 ≤ t ≤ 1 dx = 1 dt; dy = 3 dt; dz = 1 dt ∫c F·dr = ∫ (x + y) dx + xy dy  z^2 dz = ∫ (t + 3t) + 9t²  t² dt [0,1] = 14/3 → (1,3,1) to (2,1,4) x = t + 1 ; y = 3  4t ; z = 1 + 3t dx = 1 dt; dy = 4 dt; dz = 3 dt ∫c F·dr = ∫ (x + y) dx + xy dy  z^2 dz = ∫ (t + 1 + 3  4t)  4(t + 1)(3  4t)  3(1 + 3t)^2 dt [0,1] = ∫ 11t^2  17t  11 dt [0,1] = 139/6 14/3  139/6 = 37/2 Answer (2): 37/2
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.