You are feeling kind of crazy, so you are going to have the owner of the pet store randomly pick a fish for your aquarium at hom
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Parameterize the intersection by setting 
, so that
The length of the path
is then given by the line integral along ,
where
. We have
and so the line integral is
This result is fortuitous, since we can write
and so the integral reduces to
The length of the path
where
and so the line integral is
This result is fortuitous, since we can write
and so the integral reduces to