2.6 GauSs-Legendre Integration(Optional)
2.6 Gauss-Legendre Integration (Optional)
f(ad c N wn.f()+w2f(a2)
f(x)=1 ldx=2=1+2 f(x)=x:/xd=0=0101+ f()=2/ 心心 =a=l12i+2x d=0= +
1+2 101+22=
Theorem 2.8( Gauss-Legendre Two-Point Rule). If f is continuous on -1,1,the )d≈G2(f)=f()+f( 2.90) The Gauss-legendre rule G2(f) has degree of precision n=3. If fE C-1,1] the en f(x)dx≈G2)=f()+f(-5)+E2(f) (2.91) where E2(f) 135 (2.92)