Use Gauss’s divergence theorem to evaluate the surface integral ∬(xy2dydz + 2y3dxdz + y2zdxdy), where S is the closed surface consisting of the cylinder x2 +z2 = 4, 0 ≤ y ≤ 2 and two discs x2 +z2 ≤4, y=0 and x2 +z2 ≤4, y=2.

Use Gauss’s divergence theorem to evaluate the surface integral ∬(xy2dydz + 2y3dxdz + y2zdxdy), where S is the closed surface consisting of the cylinder x2 +z2 = 4, 0 ≤ y ≤ 2 and two discs x2 +z2 ≤4, y=0 and x2 +z2 ≤4, y=2.

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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Question

Use Gauss’s divergence theorem to evaluate the surface integral

∬(xy²dydz + 2y³dxdz + y²zdxdy),

where S is the closed surface consisting of the cylinder x² +z² = 4, 0 ≤ y ≤ 2 and two discs x² +z² ≤4, y=0 and x² +z² ≤4, y=2.

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