Visualizing Simpson's Rule: Area Under the Curve

[JNeutron2186]

Is there a visual way to represent this theorem? Like Riemanns rules with rectangles and trapezoids? I know the clear cut way to evaluate the area under the curve using the rule on a closed set. Soooo any thoughts?CORRECTION THIS IS SIMPSONS RULE*typo...

 

[HallsofIvy]

Just as the trapezoid rule approximates the function graph by straight lines between two consecutive points, Simpson's rule approximates the function graph by a parabola through three consecutive points.

 

[SteamKing]

Try this on for size:

http://en.wikipedia.org/wiki/Simpson's_rule

 

[JNeutron2186]

Thanks!