please solve it on paper

Denote the upper part of the hemisphere of radius 2 with center at (0, 0, 0) by S . Suppose S has upward orientation. Please do the following: . Parametrizationface. Include the domain along with your parametrization. . Calculate the flux of the vector field F(@, y, z) = (y, z, x) through the surface S. DO NOT USE THE FORMULA [10] ON PAGE 1130- MAJOR DEDUCTION FOR THIS. Make sure to write a clear, complete, and detailed solution. If you use any theorems make sure you clearly state those theorems and also show how they are justified for this