In evaluating a surface integral, I know that the surface integral of 1, dS over the surface S will give me surface area. That means that a regular double integral of the magnitude of the normal over the region R, in the xy-plane, will give the surface area. For a general sphere, x^2+y^2+z^2=a^2, can I use the normal obtained from the gradient? Or must I solve g(x,y)=sqrt(a^2-x^2-y^2) and then take the magnitude? The first way, I get that the normal is 2a and the second way I get that the normal is a/z. What is wrong?