Here is the link to the problem :

I am trying to attempt this question without using parametric form of coordinates of a circle.

So, i have taken any point (x,y) on the circle with centre(R,0).Then,

distance=sqrt( (x+R)^2 + y^2 ) …(1)

Also ,equation of the circle with centre (R,0) is (x-R)^2+y^2=R^2 …(2)

From (1) and (2), distance=sqrt( R^2+4* x *R)

Then , i have integrated 2* distance * dx with limits from 0 to 2R and divided it by 2* Pi* R.

2 because circle is symmetric about x-axis.

But , i am not getting correct answer.

Can anyone suggest whether my approach is wrong or i have taken wrong limits ?