Let be the closed surface consisting of the cylinder x² + 2² = 9 between y = 0 and y = 6 along with the disks x² + z² ≤ 9 in the plane y = 0 and in the plane y = 6 and let n be its unit outward-pointing normal vector (it is oriented outwards). Note that Σ encloses a solid region D. Evaluate the following integral: (2xî+5xĵ+7zk). ndS

Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Vectors In Two And Three Dimensions
Section9.6: Equations Of Lines And Planes
Problem 2E
Question
Let be the closed surface consisting of the cylinder x² + 2² = 9 between y = 0 and y = 6
along with the disks x² + z² ≤ 9 in the plane y = 0 and in the plane y = 6 and let n be its
unit outward-pointing normal vector (it is oriented outwards). Note that Σ encloses a solid
region D. Evaluate the following integral:
(2xî+5xĵ+7zk). ndS
Transcribed Image Text:Let be the closed surface consisting of the cylinder x² + 2² = 9 between y = 0 and y = 6 along with the disks x² + z² ≤ 9 in the plane y = 0 and in the plane y = 6 and let n be its unit outward-pointing normal vector (it is oriented outwards). Note that Σ encloses a solid region D. Evaluate the following integral: (2xî+5xĵ+7zk). ndS
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