How do i use Average Value to find the average squared distance?

Find the Average squared distance between the points of





R={(x,y): -2%26lt;=x%26lt;=2, 0%26lt;=y%26lt;=2 } and the origin.





I have no clue how. The answer is some how 8/3.|||f_ave = [ ∫ ∫ f(x,y) dA ] / [ ∫ ∫ dA ]





In this case f(x,y) is the square of the distance from the origin, i.e. (x² + y²).


Our limits/domain has already been given to us.





f_ave = [ ∫ ∫ (x² + y²) dx[-2,2] dy[0,2] ] / [ (2 - (-2)) * (2 - 0) ]


f_ave = [ ∫ ((1/3)x³ + xy²)]{x,-2,2} dy[0,2] ] / [ 8 ]


f_ave = [ 2 ∫ ((8/3) + 2y²) dy[0,2] ] / [ 8 ]


f_ave = [ ∫ ((4/3) + y²) dy[0,2] ] / [ 2 ]


f_ave = [ ((4/3)y + (1/3)y³)]{y,0,2} ] / [ 2 ]


f_ave = [ ((8/3) + (8/3)) ] / [ 2 ]


f_ave = 8/3