Question 1
Let
F = -y
i + x
j + z
k. Use Stokes's Theorem to find the flux of
curl F upward through the paraboloid

where u ∈ [0, 1] and v ∈ [0, 2π].
◦ 6π
◦ 2π
◦ 4π
◦ π
◦ 3π
Question 2
Use Stokes's Theorem to evaluate the integral

+ x
3y
2 dy + z dz, where C is the curve of intersection of the sphere

and the plane

oriented counterclockwise as seen from high on the z-axis.
◦ 0
◦ 5π
◦ 2π
◦ 4π
◦ 3π