1. The problem statement, all variables and given/known data Calculate the surface integral ∫∫S x2z2 dS, where S is the part of the cone z2=x2+y2 between the planes z=1 and z=3 2. Relevant equations There are two relative equations for calculating surface integrals by transforming them into double integrals, but my question is about the two forms of the magnitude: |ru x rv| (where r is the vector equation and u, v are parameters) and √((dg/dx)2+(dg/dy)2+1) (where x,y represent cartesian coordinates and are the parameters for g(x,y), which defines the z-coordinate). 3. The attempt at a solution I thought that the two equations were really just two different ways of expressing the same value, but due to this problem, I'm not so sure anymore. I parameterized the equation of the cone as x=r cos θ, y=r sin θ, z=r, which I believe is the correct parameterization. In using the first form of the equation, for the part that involves the magnitude of the cross product of the partial derivatives of the vector equation (which is formed by the parameterization), I yield r√2. By using the second form of the equation, I yield only √2. I've double-checked the cross product and the parameterization at least 10 times, but I still do not understand why the two forms of the same equation are giving me two different answers. Is my parameterization wrong or am I falsely thinking that the equations are really the same? Any help is appreciated!