Use the divergence theorem to evaluate the surface integral JF CFN dS where F = 10xy²zi +10yrx²zj + z²k, S is the closed hemispherical surface z = √1-x² - y² together with the disk x² + y² ≤ 1 in the xy-plane, and N is the outward unit normal for S.

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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Use the divergence theorem to evaluate the surface integral F . N dS where F = 10xy²zi + 10yx² zj + z²k, S is the closed hemispherical surface z = √1-x² - y² together with the disk
S
x² + y² ≤ 1 in the xy-plane, and N is the outward unit normal for S.
Transcribed Image Text:Use the divergence theorem to evaluate the surface integral F . N dS where F = 10xy²zi + 10yx² zj + z²k, S is the closed hemispherical surface z = √1-x² - y² together with the disk S x² + y² ≤ 1 in the xy-plane, and N is the outward unit normal for S.
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