Question

Use Simpson's rule, taking n=2, to find an approximation to \[\int\limits_{0}^{2}\sqrt{4+x ^{3}} dx\]

Answer 1

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

Answer 2

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

Answer 3

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