2.6 Gauss-Legendre integration (Optional)
2.6 Gauss-Legendre Integration (Optional)
f(a)dx a wn.f(1)+w2f(a2)
)=1: ldx=2=1+2 f(a)=. rdx=0=01x1+2x 1 f(a)=r =1x1+2 dx=o +
1+2 11 w2 e 11+2-3 3 11=-022
Theorem 2.8( Gauss-Legendre Two-Point Rule). If f s continuous on en f(x)dm≈G2()=f()+f (2.90 The Gauss-legendre rule G2(f) has degree of precision n=3. If E C[-1,1, the en (2.91 where E2(f)= 135 (2.92)