AlgCalcOne: Parabolic Splines and Archimedes (English)

This is our first serious integral calculus computation: we get the formula for the signed area of a parabolic arc, parallel to what Archimedes remarkably accomplished more than 2000 years ago, but with quite a different approach. We recover Archimedes' relation to the signed area of a maximal triangle inscribed in a parabolic arc: at least for the case of y=x^2..

https://www.youtube.com/watch?v=bPvinbhxmU0