Let S be the upper half of the unit sphere x^2+y²+z²=1 and take n as the upper unit normal. Use Stoke's theorem to find ∬ S_[(∇×v)⋅n]dσ given v(x,y,z)=3z²i+3xj−4y³k.
a) 3π
b) −3π
c)9π
d)3/2π
e) 6π
f) None of the above.