The integral ∮c(ydx - xdy) is evaluated along the

The integral ∮_c(ydx - xdy) is evaluated along the circle x² + y² = 1/4 traversed in counter clockwise direction. The integral is equal to

Given integral ∮_c (ydx - xdy)
where C is x² + y² = 1/4
Applying Green’s theorem

∮_cMdx - Ndy = ∫∫_R		δN	-	δm		dx dy
		δx		δx

where R is region included in c
∮_cydx - xdy = ∫∫_R(-1-1)dx dy
= - 2∫∫_R = –2 × Region_R
= – 2 × area of circle with radius 1/2

= 2 × π		1		²	=	-π
		2				2