Problem #1: Green's Theorem in the plane states that if C is a piecewise-smooth simple closed curve bounding a simply connected region R, and if P, O, OP/dy, and OO/Ox are continuous on R then Pdx + O dy = dx - dA. R Compute the double integral on the right hand side of Green's Theorem with P(x, y) = 2 ' Q(x, V) = and the region R enclosed by the half ellipse (x - 7)2 + (1 - 12)" = 1, y 2 12, 4 2 and the lines y = -2x + 22, and y = 2x - 6