Green's theorem - challenge problems you must submit written solutions to any two of these three problems by the due date. solu- tions will be made available after that due date. 1. find faxe-3x dx + 4(22 + y)2 dy where is the boundary of the region inside the circles x² + y2 = 2 and x2 + y2 = 9 (take c to be positively oriented). 2. find $c f. dr where f(x, y) = and c is the perimeter of x2 + y2 = 16, oriented clockwise. 3. as noted, the integral ff. di gives the flux of the vector field f across the contour c. use green's theorem to find the flux of f(x, y) = across the boundary of a circle .za + y2 = a (where a is the constant radius of the circle). take the boundary as being oriented positively.