1. The problem statement, all variables and given/known data In the attached image. 2. Relevant equations Gradient(x, y, z) * <f, g, h> = <fx, gy, hz> 3. The attempt at a solution Because the cylinder's not capped, I know that all the flux will be in the radial direction. So, I can find a normal vector by finding the gradient of the cylinder: n = <2x, 0, 2z>/(2sqrt(x^2+z^2)) = <x, 0, z>/sqrt(x^2+z^2) Now, I want to put this in terms of t (the angle) and h (y): r(t, y) = <acos(t), h, asin(t)> Where: y: (-2, 2) and t: [0, 2pi) Now we can rewrite the integrand: <acos(t)/sqrt(a), 0, asin(t)/sqrt(a)> * <acos(t)/sqrt(a), 0, asin(t)/sqrt(a)> dS =(a^2cos^2(t) + a^2sin^2(t))/a dS =a dS Now, the only thing I'm confused by (assuming everything else is right), is what to do with dS. I know it needs to be put in terms of dt and dh (where I already have the limits of integration), but I am unsure of how to perform this conversion.