Given F= [tex](ix+jy) Ln(x^2+y^2)[/tex] and given S, which is a cylinder of radius r, and height h(in the z axis) evaluate [tex] \int\int_s F.n \,ds[/tex]. It says that you shouldn't need to do any work if you think about it enough. I figured I could find the area of the main part to be [tex]2 \pi r h[/tex] then multiply that by [tex]Ln(r^2)=2Ln(r)[/tex] to get the answer but I am off by a factor of r in my answer. I don't think the caps to the cylinder contribute to this as the normal is orthogonal to F. One more question, what exactly does a surface integral return? I feel stupid but I can't seem to find out exactly what the physical meaning of the result of a surface integral is. Thanks for the help.