Let C be a simple closed smooth curve that lies in the plane x y z 1 Show that the line integral C z dx 2x dy 3ydz depends only on the area of the region enclosed by C and not on the shape of C or its location in the plane

Question: Let C be a simple closed smooth curve that lies in the plane x + y + z = 1. Show that the line integral

Let C be a simple closed smooth curve that lies in the plane x + y + z = 1. Show that the line integral
ʃ_Cz dx - 2x dy + 3ydz
depends only on the area of the region enclosed by C and not on the shape of C or its location in the plane.

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