Calculate the surface integral 1 (V × F) - dS where M is the hemisphere ² + y² + 2² = 9, π ≥ 0, with the normal in the direction of the positive x direction, and F = (0, 0, y¹)). Begin by writing down the "standard" parametrization of OM as a function of the angle (denoted by "t" in your answer), where ǝM denotes the boundary of M: x= , y = 2π Sam F ds = f(0) do, where f(0) = The value of the integral is (use "t" for theta).
Calculate the surface integral 1 (V × F) - dS where M is the hemisphere ² + y² + 2² = 9, π ≥ 0, with the normal in the direction of the positive x direction, and F = (0, 0, y¹)). Begin by writing down the "standard" parametrization of OM as a function of the angle (denoted by "t" in your answer), where ǝM denotes the boundary of M: x= , y = 2π Sam F ds = f(0) do, where f(0) = The value of the integral is (use "t" for theta).
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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Transcribed Image Text:Calculate the surface integral
x
√ (V × F) - dS where M is the hemisphere a² + y² + z² = 9, a ≥ 0, with the normal in the direction of the
positive x direction, and F = (x, 0, y¹)).
Begin by writing down the "standard" parametrization of M as a function of the angle (denoted by "t" in your answer), where ƏM denotes the
boundary of M:
X
,
y=
,2=
2πT
Sam F. ds = f(0) do, where
f(0) =
=
The value of the integral is
(use "t" for theta).
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