16-Point Gaussian Quadrature

[Gamo]

Recently I try this program called 16-Point Gaussian Quadrature found
in the HP-11C Solutions Handbook on page 30

So this program do the Integration problem. I have try diffrent problem
and the answer come out very well except one.

This one doesn't give enough accuracy when compare to the
Integration Function on the HP-15C

Here is the problem: ∫ 0 to 2 √4 - X² dx = Pi = 3.141592654

On the HP-11C and HP-15 Equation is

[X²] [4] [X<>] [-] [√]

Answer on HP-11C is 3.141722674
Answer on HP-15C is 3.141592653

So is program provided on the HP-11C Solutions Book only give three
decimal place accuracy or it only happen to certain problem.

Gamo