(a) \(\displaystyle \int_{S}{dx \wedge dy + 2zdz \wedge dx}\)

(b) \(\displaystyle \int_{C}{xdy + z^{2}dx}\)

Compare your answers and explain.

Solution:

Using spherical coordinates, I got \(\displaystyle \pi a^2\) for both parts. The only part I'm not sure about is the explanation. Is this an application of Green's Theorem?