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How to find the area between a quadratic function $f(x)=ax^2+b$ and a line $g(x)=c$?

So imagine you have the simple function $f(x)=x^2$ and the constant function $g(x)=2$ How can I find the area between the $f(x)=0$ and $f(x)=2$ without using calculous?

Marion
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  • Without using integrals ? – servabat Mar 10 '15 at 18:29
  • Yes. Without any integration. – Marion Mar 10 '15 at 18:30
  • What do you want to use then ? Do you have a specific idea or is this an open question ? – servabat Mar 10 '15 at 18:33
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    Are you allowed to use Archimedes' formula for a segment of a parabola? Or are you supposed to duplicate this? Be aware that Archimedes' method basically uses the methods of calculus, before calculus was discovered/invented, without actually using calculus. – Rory Daulton Mar 10 '15 at 18:33
  • My initial thought is that areas under graphs are defined to be the limit of the sums of strips of rectangles and so integrating is unavoidable. I could be wrong and its an interesting question. – Karl Mar 10 '15 at 18:36
  • This is nearly a duplicate: see the question (http://math.stackexchange.com/questions/305268/how-to-calculate-the-area-closed-by-a-parabola-and-a-line-without-calculus) – MPW Mar 10 '15 at 18:51
  • Yes, thanks to all. I could not remember that it was the Archimede's formula the name of what I was trying to find. Thanks. – Marion Mar 10 '15 at 19:45

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