Hello,

I don't know how to get the formula but I can give you possible way to get a valid solution:

The "centre of mass" of a plane area of homogenous material which is bounded by the x-axis, the curve of y = f(x), the straight lines

and

is the centroid of this area. The coordinates of the centroid are calculated by:

and

With your problem:

, that menas the center of the semi-circle is (0, 0),

,

Obviously

Plug in all values you know:

Use integration by substitution

Therefore the centre of mass has the coordinates