

Area of a parabolaArea under parabola & Area enclosed by parabola Archimedes, sometimes described as the inventor of integral calculus, is credited with determining a theorem & formula to find the area enclosed by a chord of a parabola.
This page: Area enclosed by a parabola 
Area enclosed by chord of parabolaFormula for thea area enclosed by the chord of a parabola Area = 2/3 area of circumscribed parallelogram formed by the chord of the parabola and a tangent of the parabola. See the picture below 