March 27, 2007 (originally conceived April 25, 2001):
Proof that a circle’s area is
Looking at only the first quadrant, we can constrain
. To get the total area, take the area found in the first quadrant and multiply by 4.
Let
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Substituting:
Move the constants across the integral:
Let
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Substituting:
Let
Substituting:
Move the constants across the integral:
Let
Substituting: