Use Green’s Theorem to find the counterclockwise circulation and outward flux for the fields and curves.

F = (2xy + x)i + (xy - y)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 = M dy-1 Outward flux N dx = J R ƏM ON + dx dy ax dy Divergence integral (4)