Flux integrals. 1. Let S denote the hemisphere x² + y²+z² = 1, z≥0, which can be written as a parameterized surface in two ways: ⚫ The spherical coordinate parameterization s(0,0)(sin cos 0, sin o sin 0, cos ) = The function graph parameterization F(x, y) = (x, y, √√1 - x² + y²) 0≤0≤2π Consider the vector field F(x, y, z) = (x, y, 0), and consider also its flux integral F.ñdS Write two different integrals for calculation of this flux integral (but don't carry through the calculations yet): ⚫ First, using the spherical coordinate parameterization • Next, using the function graph parameterization Next, • Use one of those two parameterizations to calculate the flux integral (one of those choices is better than the other). Question: What is the value of the flux integral using the other pa- rameterization? Why?
Flux integrals. 1. Let S denote the hemisphere x² + y²+z² = 1, z≥0, which can be written as a parameterized surface in two ways: ⚫ The spherical coordinate parameterization s(0,0)(sin cos 0, sin o sin 0, cos ) = The function graph parameterization F(x, y) = (x, y, √√1 - x² + y²) 0≤0≤2π Consider the vector field F(x, y, z) = (x, y, 0), and consider also its flux integral F.ñdS Write two different integrals for calculation of this flux integral (but don't carry through the calculations yet): ⚫ First, using the spherical coordinate parameterization • Next, using the function graph parameterization Next, • Use one of those two parameterizations to calculate the flux integral (one of those choices is better than the other). Question: What is the value of the flux integral using the other pa- rameterization? Why?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 33E
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Transcribed Image Text:Flux integrals.
1. Let S denote the hemisphere x² + y²+z² = 1, z≥0, which can be written
as a parameterized surface in two ways:
⚫ The spherical coordinate parameterization
s(0,0)(sin cos 0, sin o sin 0, cos )
=
The function graph parameterization
F(x, y) = (x, y, √√1 - x² + y²)
0≤0≤2π
Consider the vector field F(x, y, z) = (x, y, 0), and consider also its flux
integral
F.ñdS
Write two different integrals for calculation of this flux integral (but don't
carry through the calculations yet):
⚫ First, using the spherical coordinate parameterization
• Next, using the function graph parameterization
Next,
• Use one of those two parameterizations to calculate the flux integral
(one of those choices is better than the other).
Question: What is the value of the flux integral using the other pa-
rameterization? Why?
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