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 .

Your overall score for this problem is