Rachel bought a sheet of fifty 34-cent stamps from the post office. she paid for the stamps with a $20 bill. how much money shou
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By Green's theorem, the integral of along
is
which is 6 times the area of , the region with
as its boundary.
We can compute the integral by converting to polar coordinates, or simply recalling the formula for a circular sector from geometry: Given a sector with central angle and radius
, the area
of the sector is proportional to the circle's overall area according to
so that the value of the integral is