Help for a "Surface and Flux integrals" program

[Arno K]

If I use f(x,y)=x^2+y^2 and substite x=u*cos(v), y=u*sin(v),z=u^2 and integrate u from 0 to 1, v=0 to 2*PI I get (1/60)*(sqrt(5)*25*π+π), the same is provided by the prime, so some thing with that substitution must be wrong. Clearly my integral then has u^3*sqrt(...) which explains the difference, but where does it result from.