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Evaluate the following surface integrals. (a) || Vzds where S is the surface of the sphere a? + y? + z² = 4 above z = 1.

Evaluate the following surface integrals. (a) || Vzds where S is the surface of the sphere a? + y? + z² = 4 above z = 1.

Elementary Geometry For College Students, 7e
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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Evaluate the following surface integrals. (a) || Vzds where S is the surface of the sphere x² + y² + z² = 4 above z = 1. (b) || (x²z+y² z)dS where S is the portion of the plane z = 4+x +y inside the cylinder x² + y² = 4. (c) f(x,y, z) = x – y where S is given by z = y² for 0 <r < 1 and 0 <y < 1.
Transcribed Image Text:Evaluate the following surface integrals. (a) || Vzds where S is the surface of the sphere x² + y² + z² = 4 above z = 1. (b) || (x²z+y² z)dS where S is the portion of the plane z = 4+x +y inside the cylinder x² + y² = 4. (c) f(x,y, z) = x – y where S is given by z = y² for 0 <r < 1 and 0 <y < 1.
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