Let d be a region bounded by a simple closed path c in the xy-plane. use green's theorem to prove that the coordinates of the centroid (x, y) of d are: x = (1/2a)∫cx²dy y = (-1/2a)∫cy²dx, where a = area of d use the formulas to find the centroid of the triangle with vertices (0, 0), (a, 0), and (a, b), where a > 0 and b > 0. {x, y) = )