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IA idea #5 - Area of a parabolic segment

I"m always on the look out for interesting mathematical "nuggets" that might lead to something suitable for a student Exploration (IA task). Here is a very interesting fact about the area of a parabolic segment for a particular family of parabolas.A region bounded by a parabola and a line intersecting the parabola at two distinct points (secant line) is a parabolic segment. Consider the area of a parabolic segment for...

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