1. The problem statement, all variables and given/known data Find the value of the surface integral [tex]\int[/tex]A [tex]\bullet[/tex] da, where A = xi - yj + zk, over the surface defined by the cylinder c2 = x2 + y2. The height of the cylinder is h. 2. Relevant equations I found the answer quite easily using Gauss's theorem, as the divergence of the vector A is simply 1, so the volume integral reduces to [tex]\int[/tex]dv, which just becomes the volume of the cylinder. However, I was wondering how to integrate directly without using Gauss's theorem; i.e., integrate the original surface integral [tex]\int[/tex]A [tex]\bullet[/tex] da. I feel like this is a pretty simple question and I'm thinking way too hard.