Surface Integral
A surface integral is an integral along a smooth curve C.
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Description
Given a smooth surface S, integrating a function f along S gives the scalar surface integral. As the name implies, this returns a scalar value.
Parameterize f using r(u,v) to get:
where r = [x(u,v) y(u,v) z(u,v)], ru = [∂x/∂u ∂y/∂u ∂z/∂u], and rv = [∂x/∂v ∂y/∂v ∂z/∂v].
This gives a straightforward calculation for surface area:
