Let
F(x,y,z)=e xy
i+e xz
j+x 2
zk
and let
S
be the half of the ellipsoid
4x 2
+y 2
+4z 2
=4
that lies to the right of the
xz
-plane, oriented in the direction of the positive
y
-axis. Use Stokes' Theorem to evaluate
∬ S

curlF⋅dS