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Consider the vector field F = (2x, 3y, 4z) and the surface z = z = 4-2² - y², z 20. Write down the line integral and the surface integral that Stokes' Theorem tells us are equal for this vector field and surface. Evaluate both. Hint: The surface integral requires very little work. You do not even need to parameterize the surface

Consider the vector field F = (2x, 3y, 4z) and the surface z = z = 4-2² - y², z 20. Write down the line integral and the surface integral that Stokes' Theorem tells us are equal for this vector field and surface. Evaluate both. Hint: The surface integral requires very little work. You do not even need to parameterize the surface

Advanced Engineering Mathematics
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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just stokes thm part pls

Consider the vector field F = (2x, 3y, 4z) and the surface z = 4-2² - y², 220. Write down the line integral and the surface integral that Stokes' Theorem tells us are equal for this vector field and surface. Evaluate both. Hint: The surface integral requires very little work. You do not even need to parameterize the surface.
Transcribed Image Text:Consider the vector field F = (2x, 3y, 4z) and the surface z = 4-2² - y², 220. Write down the line integral and the surface integral that Stokes' Theorem tells us are equal for this vector field and surface. Evaluate both. Hint: The surface integral requires very little work. You do not even need to parameterize the surface.
Expert Solution
Step 1

The given vector field is F=<2x,3y,4z>, and the surface is z=4-x2-y2, z≥0.

We have to verify Stoke's theorem.

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