17.3

1.
divF=0
IntIntS F*dS=0

3.
divF=2
IntIntS F*dS=2*Pi*1^2*2=4Pi

5.
divF=z^2
Int(Int(Int(z^2,z=-sqrt(1-x^2-y^2)..sqrt(1-x^2-y^2)),y=-sqrt(1-x^2)..sqrt(1-x^2)),x=-1..1)
=Int(Int((2*(-x^2-y^2+1)^(3/2))/3,y=-sqrt(1-x^2)..sqrt(1-x^2)),x=-1..1)
=Int((Pi(x^2-1)^2*(-sign(x^2-1))^1/4)/4,x=-1..1)
=4Pi/15

7.
divF=y^2+z^2+x^2
Int(Int(Int(y^2+z^2+x^2, z=0..3),y=-sqrt(2-x^2)..sqrt(2-x^2)), x=-2..2)
=Int(Int(3x^2+3y^2+9,y=-sqrt(4-x^2)..sqrt(4-x^2)), x=-2..2)
=Int(2*(4-x^2)^(3/2)+6*(x^2+3)*sqrt(4-x^2), x=-2..2)
= 60Pi

11.
divF=3x^2+3z^2
Int(Int(Int(3x^2+3z^2,z=0..sqrt(4-x^2-y^2)),y=0..sqrt(4-x^2)),x=0..2)
=Int(Int((-x^2-y^2+4)^(3/2)+3x^2*sqrt(-x^2-y^2+4),y=0..sqrt(4-x^2)),x=0..2)
=Int((-3*Pi*(x^2-4)*(3x^2+4)(-sign(x^2-4))^1/4)/16,x=0..2)
=Int((-3*Pi*(x^2-4)*(3x^2+4)(-sign(x^2-4))^1/4)/16,x=0..2)
=32Pi/5

15.
divF=2
Int(Int(Int(2,z=0..9)y=-sqrt(9-x^2)..sqrt(9-x^2)),x=-3..3)
=Int(Int(18,y=-sqrt(9-x^2)..sqrt(9-x^2)),x=-3..3)
=Int(36*sqrt(9-x^2),x=0..3)
=81Pi