21. Use Stokes' theorem to evaluate (curl F.N)ds, where F(x, y, z) = x î + y² ĵ + zezy and S is the part of surface z = 1 - x² – 2y² with z ≥ 0, oriented counterclockwise.
21. Use Stokes' theorem to evaluate (curl F.N)ds, where F(x, y, z) = x î + y² ĵ + zezy and S is the part of surface z = 1 - x² – 2y² with z ≥ 0, oriented counterclockwise.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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21
![**Problem 21:**
Use Stokes' theorem to evaluate the surface integral:
\[
\iint_S (\text{curl} \, \mathbf{F} \cdot \mathbf{N}) \, dS
\]
where the vector field \(\mathbf{F}(x, y, z) = x \, \mathbf{i} + y^2 \, \mathbf{j} + xe^{xy} \, \mathbf{k}\) and \(S\) is the part of the surface defined by the equation \(z = 1 - x^2 - 2y^2\) with \(z \geq 0\), oriented counterclockwise.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F07dc3289-c262-41f1-9fc5-a8d18500de1b%2F5b432824-8d12-4a05-92e2-7118301b85da%2Fb29zu1j_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 21:**
Use Stokes' theorem to evaluate the surface integral:
\[
\iint_S (\text{curl} \, \mathbf{F} \cdot \mathbf{N}) \, dS
\]
where the vector field \(\mathbf{F}(x, y, z) = x \, \mathbf{i} + y^2 \, \mathbf{j} + xe^{xy} \, \mathbf{k}\) and \(S\) is the part of the surface defined by the equation \(z = 1 - x^2 - 2y^2\) with \(z \geq 0\), oriented counterclockwise.
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