Simplify the expression ((2x^2y)^3/(3xy^3)^2)^2
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We can parameterize this part of the cylinder using
with
and 
. Then the surface element is
so the area is given by the surface integral, where
denotes the part of the cylinder in question,
Probably less work would involve a simpler geometric approach, but it doesn't hurt to practice setting up a proper surface integral.
with
so the area is given by the surface integral, where
Probably less work would involve a simpler geometric approach, but it doesn't hurt to practice setting up a proper surface integral.