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## Main Question or Discussion Point

Why is it that when we evaluate a surface integral of:

f(x, y ,z) over dS, where

x = x(u, v)

y = y(u, v)

z = z(u, v)

dS is equal to ||

Why don't we use the jacobian here when we change coordinate systems?

f(x, y ,z) over dS, where

x = x(u, v)

y = y(u, v)

z = z(u, v)

dS is equal to ||

**r**_{u}X**r**_{v}|| dAWhy don't we use the jacobian here when we change coordinate systems?