2. Let S C R² be the unit square: = {x € R² : 0 < x₁ < 1, 0 < x₂ < 1}. Define x2 F: → R² by X2 = [X₁²+²x₂] x2 Verify that the divergence theorem holds for this domain 2 and this vector field F. F(x)= 1
2. Let S C R² be the unit square: = {x € R² : 0 < x₁ < 1, 0 < x₂ < 1}. Define x2 F: → R² by X2 = [X₁²+²x₂] x2 Verify that the divergence theorem holds for this domain 2 and this vector field F. F(x)= 1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![2. Let CR² be the unit square: № = {x € R² : 0 < x₁ < 1, 0 < x2 < 1}. Define
F:→ R² by
x2
= [X₁ + ² x ₂ ] ₁
x2
Verify that the divergence theorem holds for this domain 2 and this vector field F.
F(x)=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc7559a47-bb34-494d-9e33-22c98791555e%2F54c14591-aace-40e7-a37c-0b9655d2fcb6%2Fvnavfja_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Let CR² be the unit square: № = {x € R² : 0 < x₁ < 1, 0 < x2 < 1}. Define
F:→ R² by
x2
= [X₁ + ² x ₂ ] ₁
x2
Verify that the divergence theorem holds for this domain 2 and this vector field F.
F(x)=
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