Find the exact values of the Gauss points 0

x1
x2
x3
4 and weights for n=3. Use the derivation given

Question

Find the exact values of the Gauss points 0x1x2x34 and weights for n=3. Use the derivation given

in class, but work over the interval [0,4]. The Gauss points for a given value of n will be the zeros of the polynomial of degree n that is obtained by using Gram-Schmidt on the standard power function basis for the polynomials, and requiring each of the orthogonal basis polynomials to take on the value 1 when evaluated at x=1

:−
3 = {1, ,
ℎ , } [0,4] ℎ
( ) = 1, ( )= = ( )= − ; , ( )gt;
; ( ), ( ) gt; − − ∫ ; , ( )gt;
; ( ), ( ) gt; = − = − ∫
∫ ; , ( )gt;
; ( ), ( ) gt;
−4…
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