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Use Stoke's Theorem to evaluate (V x F). dS where M is the hemisphere x² + y² + z² = 9, x ≥ 0, with the normal in the M direction of the positive x direction, and F = (x5, 0, y¹). Begin by writing down the "standard" parametrization of OM as a function of the angle (denoted by "t" in your answer) Ꮎ X = , y = ,Z = SOM F. ds = √2 f(0) do, where f(0) = The value of the integral is (use "t" for theta).

Use Stoke's Theorem to evaluate (V x F). dS where M is the hemisphere x² + y² + z² = 9, x ≥ 0, with the normal in the M direction of the positive x direction, and F = (x5, 0, y¹). Begin by writing down the "standard" parametrization of OM as a function of the angle (denoted by "t" in your answer) Ꮎ X = , y = ,Z = SOM F. ds = √2 f(0) do, where f(0) = The value of the integral is (use "t" for theta).

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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Use Stoke's Theorem to evaluate (V x F). dS where M is the hemisphere x² + y² + z² = 9, x ≥ 0, with the normal in the M direction of the positive x direction, and F = (x5, 0, y¹ ). Begin by writing down the "standard" parametrization of OM as a function of the angle (denoted by "t" in your answer) X = , y = Z = JOM F. ds f(0) The value of the integral is = Σπ ² f(0) do, where = (use "t" for theta).
Transcribed Image Text:Use Stoke's Theorem to evaluate (V x F). dS where M is the hemisphere x² + y² + z² = 9, x ≥ 0, with the normal in the M direction of the positive x direction, and F = (x5, 0, y¹ ). Begin by writing down the "standard" parametrization of OM as a function of the angle (denoted by "t" in your answer) X = , y = Z = JOM F. ds f(0) The value of the integral is = Σπ ² f(0) do, where = (use "t" for theta).
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