4. Show that the line integral of F = [0, z] around a closed curve in the r- y plane, oriented as in Green's Theorem, measures the area of the region enclosed by the curve. Additionally, find two more vector fields G, H that satisfy the same property as F: the vector circulation around a simple closed curve C equals the area of the region enclosed by C. Explain.
4. Show that the line integral of F = [0, z] around a closed curve in the r- y plane, oriented as in Green's Theorem, measures the area of the region enclosed by the curve. Additionally, find two more vector fields G, H that satisfy the same property as F: the vector circulation around a simple closed curve C equals the area of the region enclosed by C. Explain.
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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![4. Show that the line integral of F = [0, x] around a closed curve in the r - y plane,
oriented as in Green's Theorem, measures the area of the region enclosed by the curve.
Additionally, find two more vector fields G, Ħ that satisfy the same property as F:
the vector circulation around a simple closed curve C equals the area of the region
enclosed by C. Explain.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F690bc708-737a-4036-8bde-cd8ee17ec8dd%2F56027f7c-8df4-4aa4-8f5c-8917f186cddf%2Fu93982f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. Show that the line integral of F = [0, x] around a closed curve in the r - y plane,
oriented as in Green's Theorem, measures the area of the region enclosed by the curve.
Additionally, find two more vector fields G, Ħ that satisfy the same property as F:
the vector circulation around a simple closed curve C equals the area of the region
enclosed by C. Explain.
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