which of the given expressions are equivalent?select all that apply.3z+2z and 5z, {8x-8x}-y and 0,9.1 +4.5a-2.5a and 11.1a,-7y[3
2 answers:
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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