Surface
Integrals (continued)
Also note the partial
derivatives ru
= ∂ r / ∂ u and
rv = ∂ r / ∂ v Now the element of surface
area is dS = | ru du x rv dv | = | ru x rv
| du dv but
ru x rv = N = normal to the surface, S and du dv = dA So the relation between
the element of surface area, dS, and the
element of area, dA is dS = | N |
dA
(See the figure below) |
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