Centroid of a Region

Question

The centroid of a region R in the xy-plane is the point {SuperStar[x], SuperStar[y]} where
SuperStar[x] is the average value of f[x,y] = x on R and
SuperStar[y] is the average value of g[x,y] = y on R.
Calculate the centroid of the rectangle R consisting of the points with -3 ≤ x ≤ 3 and -2 ≤ y ≤ 2.

Answer 1

Average ( f(x,y)) on [-3,3]  = double integral f(x,y) dy dx  , y=[-2,2], x=[-3,3] 

 

Average ( g(x,t)) on [-2,2 ] = double integral g(x,y) dx dy , x=[-2,2], y = [-3,3]