i) Evaluate the surface integral where F = (x,y,zx) and S has upward orientation. S is the part of the paraboloid Z= 2-- above the square 0

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.6: The Three-dimensional Coordinate System
Problem 41E: Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?
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Q2 both parts solve take your time
2.
i) Evaluate the surface integral
F - aš
where F = (x, y, zx) and S has upward orientation. S is the part of the paraboloid Z = 2-x? -y° above the
square 0<x<1,0<y<1.
(ii) Find the flux of the vector field F = (z, zy, x) across of the upper hemisphere (with upward orientation)
x² +y? +z? = 4 with z 20. (Hint: parametrize the surface).
Transcribed Image Text:2. i) Evaluate the surface integral F - aš where F = (x, y, zx) and S has upward orientation. S is the part of the paraboloid Z = 2-x? -y° above the square 0<x<1,0<y<1. (ii) Find the flux of the vector field F = (z, zy, x) across of the upper hemisphere (with upward orientation) x² +y? +z? = 4 with z 20. (Hint: parametrize the surface).
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