Question

Use Stokes' theorem to evaluate S ∇ ✕ F · n̂ dS where F = 8y2z, 3xz, 6x2y2 and S is the paraboloid z = x2 + y2 inside the cylinder x2 + y2 = 1, oriented upward.

Name: use stokes theorem to evaluate s f n ds where f 8y2z 3xz 6x2y2 and s is the paraboloid z x2 y2 inside the cylinder x2 y2 1 oriented upward 53947
Uploaded: 2023-08-18T11:52:05-08:00
Duration: 4 min 26 s
Channel: Madhur L
Description: use stokes theorem to evaluate s f n ds where f 8y2z 3xz 6x2y2 and s is the paraboloid z x2 y2 inside the cylinder x2 y2 1 oriented upward 53947

          Use Stokes' theorem to evaluate 
  S
 ∇ ✕ F · n̂ dS
where 
F = 
8y2z, 3xz, 6x2y2
and S is the paraboloid 
z = x2 + y2
inside the cylinder 
x2 + y2 = 1,
oriented upward.

Added by Philip V.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

08/18/2023

Step 1

To evaluate the surface integral \( \iint_S \nabla \times \mathbf{F} \cdot \hat{n} \, dS \) using Stokes' theorem, we will follow these steps: Show more…

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Use Stokes' theorem to evaluate S ∇ ✕ F · n̂ dS where F = 8y2z, 3xz, 6x2y2 and S is the paraboloid z = x2 + y2 inside the cylinder x2 + y2 = 1, oriented upward.