How to find the average squared distance between the points of the unit disk and the point (1,1)

The unit disk can be parameterized by the function



where and . The squared distance between any point in this region and the point (1, 1) is






The average squared distance is then going to be the ratio of [the sum of all squared distances between every point in the disk and the point (1, 1)] to [the area of the disk], i.e.