There is no dr here since radius of sphere does not change. The easiest way is to move to spherical coordinates. You integrate with respect to Pi and theta.
find the area of the portion of the sphere z=(1-x^2-y^2)^(1/2) which lies between z=0 and z=1?
that would be the double integral dS where dS is the area element of S.
i tried to parametrise it then from
double integral dS to integrate from r=0 to 1 then integrate from phi = 0 to pi drdphi...
may i know what is wrong with my working?