A farmer wants to fence an area of 6 million square feet in a rectangular field and then divide it in half with a fence parallel
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I assume has counterclockwise orientation when viewed from above.
By Stokes' theorem,
so we first compute the curl:
Then parameterize by
where the -component is obtained from
with and
.
Take the normal vector to to be
Then the line integral is equal in value to the surface integral,