The figure shows a parabolic segment, that is, a portion of a parabola cut off by a chord AB. It also shows a point C on the parabola with the property that the tangent line at C is parallel to the chord AB. Archimedes proved that the area of the parabolic segment is 4/3 times the area of the inscribed triangle ABC. Verify Archimedes’ result for the parabola y = 4 – x² and the line y = x + 2.

Transcribed Image Text:

A с B