1. The problem statement, all variables and given/known data Basically, I am being asked to calculate the electric flux through the top of a hemisphere centered on the z-axis using "brute force integration" of the surface area. 2. Relevant equations Gauss' Law 3. The attempt at a solution Using intuition and Gauss' law, I know that the flux is Φ=Eπr^2, but I'm not sure how to prove this using "brute force" integration as my teacher requires. If anyone could help me at least set up the integral, it would be much appreciated.