Use Green’s Theorem to find the counterclockwise circulation and outward flux for the field F and curve C.

F = (x - y)i + (y - x)j

C: The square bounded by x = 0, x = 1, y = 0, y = 1

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THEOREM 5-Green's Theorem (Flux-Divergence or Normal Form) Let C be a piecewise smooth, simple closed curve enclosing a region R in the plane. Let F = Mi + Nj be a vector field with M and N having continuous first partial derivatives in an open region containing R. Then the outward flux of F across C equals the double integral of div F over the region R enclosed by C. = fr-nds-May- Outward flux - N dx = JI ( T ax R = aM ƏN dy Divergence integral dx dy (4)