SOLUTION: Find the area bounded by the curve r=2acos(θ)

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Question 404203: Find the area bounded by the curve r=2acos(θ)
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
For polar coordinates, the area would be given by the integral

=a%5E2int%28%28cos%282theta%29+%2B+1%29%2C+d%28theta%29%2C+0%2C+pi%29
=a%5E2%28sin%282theta%29%2F2+%2B+theta%29%5B0%5D%5E%28pi%29%29
= a%5E2%28sin%282pi%29%2F2+%2B+pi+-+sin0%2F2+-+0%29
= a%5E2pi
NOTE: The polar equation is equivalent to the circle %28x+-+a%29%5E2+%2B+y%5E2+=+a%5E2, after changing to rectangular coordinates.
A direct calculation of the area of this circle using the formula A+=+pi%2Ar%5E2
would give the same answer a%5E2pi.