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?

  • $\begingroup$ Without using integrals ? $\endgroup$
    – servabat
    Commented Mar 10, 2015 at 18:29
  • $\begingroup$ Yes. Without any integration. $\endgroup$
    – Marion
    Commented Mar 10, 2015 at 18:30
  • $\begingroup$ What do you want to use then ? Do you have a specific idea or is this an open question ? $\endgroup$
    – servabat
    Commented Mar 10, 2015 at 18:33
  • 1
    $\begingroup$ 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. $\endgroup$ Commented Mar 10, 2015 at 18:33
  • $\begingroup$ 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. $\endgroup$
    – Karl
    Commented Mar 10, 2015 at 18:36


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