Chapter 8.8, Problem 63E

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)

From the previous exercise, $S_2^{2j}={\displaystyle \underset{x_{2j}}{\overset{x_{2j+2}}{\int }}f(x)dx}$if $f$ is a quadratic polynomial. Use the previous solution to show that $S_N$ is exact for all $N$if $f$is a quadratic polynomial.