If R is a closed bounded region in the xy-plane whose boundary curve is C with arc lengths and outward normal ñ: i- Show that Green's theorem in the plane may be written as F.ñ ds = •ñ ds=ffdiv F dxdy C R ii- Verify the result in (i) for F=7x1-3yj and C the circle x² + y² = 4.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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If R is a closed bounded region in the xy-plane whose boundary curve is C with arc
lengths and outward normal ñ :
i- Show that Green's theorem in the plane may be written as
[F•ñ
JF.ñ ds = ffdiv F dxdy
C
R
ii- Verify the result in (i) for F = 7x1-3yj and C the circle x² + y² = 4.
Mark
Transcribed Image Text:If R is a closed bounded region in the xy-plane whose boundary curve is C with arc lengths and outward normal ñ : i- Show that Green's theorem in the plane may be written as [F•ñ JF.ñ ds = ffdiv F dxdy C R ii- Verify the result in (i) for F = 7x1-3yj and C the circle x² + y² = 4. Mark
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