Let D be a region bounded by a simple closed path C in the xy-plane. The coordinates of the centroid х, у of D are given below, where A is the area of D.
X = 1 2A x² dy у y-- 1 y2 2A IC 2 dx
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) = ) X
Use Green's Theorem to evaluate the line integral along the given positively oriented curve. 1. (5y + 7eVx) dx + (10% 10x + 7 cos(y2)) ay C is the boundary of the region enclosed by the parabolas y = x2 and x = y?
