The Speedy Fast Ski Resort has started to keep track of the number of skiers and snowboarders who bought season passes.The Ratio
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Compute the curl of :
By Stoke's theorem, the (line) integral of along
is equivalent to the (surface) integral (or flux) of
across
, the oriented surface with boundary
.
Take to be the part of the plane
within the cylinder
. Parameterize
by
with and
. Take the normal vector to
to be
Then the integral is