Let C be a simple closed smooth curve in the plane 2x + 2y + z = 2, oriented as shown here. Show that 2y dx + 3z dy – x dz 2x + 2y + z = 2 -2 1 depends only on the area of the region enclosed by C and not on the position or shape of C.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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Let C be a simple closed smooth curve in the plane
2x + 2y + z = 2, oriented as shown here. Show that
2y dx + 3z dy – x dz
2x + 2y + z = 2
-2
1
depends only on the area of the region enclosed by C and not on
the position or shape of C.
Transcribed Image Text:Let C be a simple closed smooth curve in the plane 2x + 2y + z = 2, oriented as shown here. Show that 2y dx + 3z dy – x dz 2x + 2y + z = 2 -2 1 depends only on the area of the region enclosed by C and not on the position or shape of C.
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