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prove you cannot integrate using circles?
in other words, prove that by summing the areas of an infinite number of circles under a curve, you cannot produce the exact area under the curve.
1 Answer
- SassafrasLv 41 decade agoFavorite Answer
I'm assuming you are talking about putting an infinite number of infinitesimal circles adjacent to each other.
The problem is that with circles there will always be the area outside of the circle. Imagine a circle in a square the area of the square that is outside the circle will never be counted.
The area of a square is (2r)^2
The area of a circle is pi*r^2
The ratio of the area of a circle to a square is:
pi*r^2/ (2r)^2
simplify:
Ratio = pi / 4
I would think you could integrate using circles if you multiplied your result by the inverse of this ratio, 4/pi.
