i have been told that simpson with 3 points is a single panel
??
why??
a pannel is the distance between to points
so if we have 3 points then we have 2 panels
??
http://i48.tinypic.com/nlc4t1.jpg
No, a "panel", in the sense that you are using it here, is the region over which we have a single "piece" of our piecewise quadratic that we are using to approximate the actual function to be integrated.
In "Riemann sums" we use a "piecewise constant" function between two points and in the "trapezoid method" we use a "piecewise constant" approximation, again between two points because two points determine a line. In both of those case a "panel" is the region between two given points.
But in "Simpson's rule" we use a "piecewise quadratic" function. A quadratic function is of the form " " which, because it requires us to determine the three coefficients, a, b, and c, requires three points. For Simpson's rule, a "panel" ranges over three points, not two.