Consider a circle (radius R) to be made up of many concentric rings of radius r and thickness dr. Find the area, dA, of one of t
hese rings and integrate from 0 to R to get the area of the circle. Remember, the area of a very thin ring is just the circumference times the thickness. For something a bit more challenging, try to set it up as a sum of thin parallel bars rather than a sum of rings.
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