Chapter 6.9, Problem 9P

Apply Green’s theorem with $P=0,Q=\frac{1}{2}{x}^2$ to the triangle with vertices $(0,0)$, (0,3), (3,0). You will then have ${\displaystyle \iint x}dxdy$ over the triangle expressed as a very simple line integral. Use this to locate the centroid of the triangle. (Compare Chapter $5,\text{ Section }3.)$