Calculate the surface integral (V × F) · dS where M is the hemisphere x2 + y? + z2 = 9, x > 0, with the normal in the direction of the positive x direction, and F = (x³, 0, y')). Begin by writing down the "standard" parametrization of aM as a function of the angle 0 (denoted by "t" in your answer) x = 0 , y = 3cost 3sint Say F. ds = " f(0) d0, where f(0) (use "t" for theta). The value of the integral is ||
Calculate the surface integral (V × F) · dS where M is the hemisphere x2 + y? + z2 = 9, x > 0, with the normal in the direction of the positive x direction, and F = (x³, 0, y')). Begin by writing down the "standard" parametrization of aM as a function of the angle 0 (denoted by "t" in your answer) x = 0 , y = 3cost 3sint Say F. ds = " f(0) d0, where f(0) (use "t" for theta). The value of the integral is ||
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
(V × F) · dS where M is the hemisphere
x2 + y? + z2 = 9, x > 0, with the normal in the direction of the positive x direction,
and F = (x³, 0, y')).
Begin by writing down the "standard" parametrization of aM as a function of the angle 0
(denoted by "t" in your answer)
x = 0
, y = 3cost
3sint
Say F. ds = " f(0) d0, where
f(0)
(use "t" for
theta).
The value of the integral is
||
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