Compute the integral $\int_{S^2} zdx\wedge dy$ in two ways: First using spherical coordinates and second using the parameterization of the hemispheres using square roots.

  • $\begingroup$ it is a nice problem... what had you done so far? $\endgroup$ – janmarqz Nov 7 '16 at 17:47
  • $\begingroup$ I really do not know where to begin.... I am totally stuck. of course I know the spherical coordinates $x=r\sin\theta \cos\varphi,~ y=r \sin\theta\sin\varphi, ~ z=r\cos\theta$. $\endgroup$ – The Triforce Nov 7 '16 at 19:37

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