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Use Stokes' Theorem to evaluate[math] where [math] is the
hemisphere [math], with the
normal in the direction of the positive x direction, and
[math].
Begin by writing down the "standard" parametrization of [math] as a function of the angle [math] (denoted by "t" in your answer)
[math]
, [math]
, [math]
.
[math], where
[math]
(use "t" for theta).
The value of the integral is
.