Flux integrals.1. Let S denote the hemisphere x² + y²+z² = 1, z≥0, which can be writtenas a parameterized surface in two ways:⚫ The spherical coordinate parameterizations(0,0)(sin cos 0, sin o sin 0, cos )=The function graph parameterizationF(x, y) = (x, y, √√1 - x² + y²)0≤0≤2πConsider the vector field F(x, y, z) = (x, y, 0), and consider also its fluxintegralF.ñdSWrite two different integrals for calculation of this flux integral (but don'tcarry through the calculations yet):⚫ First, using the spherical coordinate parameterization• Next, using the function graph parameterizationNext,• 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?

Answered: Image /qna-images/answer/46012316-1303-4cd9-9183-c1cdac58c85a.jpg

Answered: Flux integrals. 1. Let S denote the…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.5: Polar Coordinates

Problem 98E

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