## anonymous 5 years ago Use Simpson's rule, taking n=2, to find an approximation to $\int\limits_{0}^{2}\sqrt{4+x ^{3}} dx$

1. anonymous

h/3[f(0)+2f(2)+4f(1)+f(2)] h=2-0)/2=1 f(0)=2,f(1)=sqrt(5),f(2)=sqrt(12) (2+3sqrt(12)+4sqrt(5))/3=7.11219225

2. anonymous

i think the coefficient we can only use in n=2 are 1 4 1 therefore A=(h/3)(f(0)+4f(1) +f(2)) =(1/3)(2+4sqrt5+2sqrt3)=4.80279

3. anonymous

I thought simpson's rule was h/3(f(0) +4f(1)+2f(2))