PROJECT. Other Forms of Green's Theorem in the Plane. Let
Chapter 10, Problem 10.4(choose chapter or problem)
PROJECT. Other Forms of Green's Theorem in the Plane. Let Rand C be as in Green's theorem, r' a unit tangent vector. and n the outer unit normal vector of C (Fig. 238 in Example 4). Show that (1) may be written or (12) I I(CUrIF)OkdXdy = f For' ds R C (11) I I div F dx dy = f F 0 n ds R C where k is a unit vector perpendicular to the xy-plane. Velify (11) and (12) for F = [7x, - 3)'] and C the circle x 2 + )'2 = 4 as well as for an example of your own choice.
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