S is the set of points with coordinates ( r.cost ; r.sint ; r.sint + 3 ), where (r;t) are the polar coordinates : 0<r<1 and 0<t<2.pi
dS = 2r.dr.dt
I is the integral from r = 0 to 1, from t = 0 to 2.pi, of 2.r^2.sint(r.sint + 3) = 2.r^3.(sint)^2 + 6r^2.sint
Evaluate first the integral along t :
integral of sint gives 0,
integral of (sint)^2 gives pi.
Leaving you with integral from 0 to 1 of 2.pi.r^3.
Finally, I = pi/2
This post was edited by feanur on May 15 2015 02:32am