Q: Let S be the surface of the paraboloid of revolution z = 1 − x² − y² with the domain of definition x² + y² ≤ 1, and let Γ be the boundary of the paraboloid. Given: F = x³i + (x + y − z)j + yzk. What is the value of ∬_S curl F · dS?
(a)2π
(b)π
(c)π/2
(d)π²
Correct Answer: (b)
Detailed explanation coming soon.