Verify the Divergence Theorem for the vector field F = (r² = z)i + (y² - x)j + (2²-y)k where R is the region bounded by z = 1-r² - y² and z = 0. (Note that the surface may be decomposed into two smooth pieces, S₁ and S₂.)

Verify the Divergence Theorem for the vector field F = (r² = z)i + (y² - x)j + (2²-y)k where R is the region bounded by z = 1-r² - y² and z = 0. (Note that the surface may be decomposed into two smooth pieces, S₁ and S₂.)

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.FOM: Focus On Modeling: Vectors Fields

Problem 11P

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Question

Please Please include both left hand side and right hand side for this problem.

(Also if you can separately integrate please work on that separately and clearly indicate which is which)

Also if you are using paper please write in neat handwriting

Verify the Divergence Theorem for the vector field F = (x² - z)i + (y² - x)j + (2²-y)k where R is
the region bounded by z = 1-r² - y² and z = 0. (Note that the surface may be decomposed into two
smooth pieces, S₁ and S₂.)

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2. Verify the Divergence Theorem for the vector field F = (x²-z)i + (y² - x)j+z²k where R is the region bounded by z = 1- x² - y² and z = 0. (Note that the surface may be decomposed into two smooth pieces, S₁ and S2.)