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**Zirtco** Thanks for that explanation. It makes sense. But here is what I'm still confused about: for the second problem that I couldn't solve with the cone in the first quadrant, how was I to know not to use r vectors and not to have dS equal ||Rx x Ry||? If they make you integrate fdS, what exactly are you integrating graphically? If anyone could explain when to use these methods, it'd be fantastic:

1. dS = ||Rx x Ry||

2. dS = sqrt((∂f/∂x)^2 + (∂f/∂y)^2 + 1)

3. ndS = (-Fx, -Fy, 1)

When to use each of these methods? And what do each of them mean in 3D? A million thanks!