Chapter 7.7, Problem 32E

(a) A table of values of a function g is given. Use Simpson’s Rule to estimate ${\displaystyle {\int }_0^{1.6}g\left(x\right)dx}$.

x	g(x)
0.0	12.1
0.2	11.6
0.4	11.3
0.6	11.1
0.8	11.7
1.0	12.2
1.2	12.6
1.4	13.0
1.6	13.2

(b) If $-5\le g^{\left(4\right)}\left(x\right)\le 2$ for $0\le x\le 1.6$, estimate the error involved in the approximation in part (a).