Chapter 8.9, Problem 61E

To determine

(a)

To show that $S_N$ is the sum of the approximations on the intervals $[x_{2j},x_{2j+2}]$ that is $S_N$ = $S_2^0+S_2^2+\mathrm{...}+S_2^{N-2}$

To determine

(b)

$S_2^{2j}={\displaystyle \underset{x_{2j}}{\overset{x_{2j+2}}{\int }}f(x)dx}$ if $f$ is a quadratic polynomial. To show that $S_N$ is exact for all $N$ if $f$ is a quadratic polynomial