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Use Green's Theorem to evaluate f F - dr. (Check the orientation of the curve before applying the theorem.) C F(x, y) = (y cos(y), x sin(y)), C is the circle (X 3)2 + (y + 2)2 = 9 oriented clockwise -x Need Help? 10. [1/3 Points] DETAILS PREVIOUS ANSWERS SCALC8 16.4.021. (a) If C is the line segment connecting the point (x1, y1) to the point (x2, y2), find the following. c x dy - y dx X1/2 - X21 (b) If the vertices of a polygon, in counterclockwise order, are (x1, y1), (X2, y2), . .., (Xn, Yn), find the area of the polygon. OA = = (X2/1 - X1/2) + (X3/2 - X2/3) + ...+ (Xnyn-1 - Xn-1) + (X1yn- Xny1) O A = = (X1/2 - X2y1) + (X2/3 - X3/2) + ... + (Xn-1 - Xnyn- 1) + (Xny1 - x1yn) O A = = (X172 - X2/1) - (X2/3 - X3/2) - ... - (Xn - 1 - Xnyn - 1) + (Xny1 - x1yn) OA = = ( X1/2 + X2y1) + (X2/3 + X3/2) + ...+ (Xn- 1 + Xnyn- 1) + (Xny1 + x1yn) A = (X1/2 - X2y1) + (X2/3 - X32) + ...+ (Xn-1yn -Xnyn- 1) + (Xny1 -X1yn) X (c) Find the area of the pentagon with vertices (0, 0), (2, 1), (1, 4), (0, 3), and (-3, 1). 9pi