Now you'll evaluate the integral ∫c7ycos(6x)dx+2xydy on the closed curve c consisting of the line segments from (0,0) to (5,7) to (0,7) to (0,0) using green's theorem. green's theorem says this integral can be rewritten in the form ∫∫df(x, y)da in this integral, f(x, y) = (7/6)ysin(6x) setting up the double integral over the region d, you get