1. The problem statement, all variables and given/known data Calculate §§ A.n dS if A= 2y(x^2)i-(y^2)j + 4xzk over the region in the first octant bounded by (y^2)+(z^2) = 9 and x = 2 2. Relevant equations 3. The attempt at a solution Let n = (yj + zk) / 3 then A.n = [-(y^3) +4xz^3] / 3 Since we 'll project the surface onto the xy-plane: |n.k| = z/3 and z = SQRT(9-y^2) Putting all together I obtain = §§R (4xz^3 - (y^3))/z dx dy Now making the appropriate changes and setting up the limits of integration: §y=30 §x=20 4x(9-y^2) - (y^3)/sqrt(9-y^2) dx dy However I always obtain 108 as a result and not 180 as my book suggested me (and after verification by Gauss' divergence theorem. Is there a problem with the limits of integration? Wrong projection? I really have no clue ... Thanks for the help!