## Calculus (3rd Edition)

Error $(S_2)=0$, so $S_2$ gives the exact value of the integral.
Error $(S_N) \leq \dfrac{k_4(b-a)^3}{180N^4}$ For $N=2$, we have: Error $(S_N) \leq \dfrac{k_4(b-a)^3}{180N^4} \\ \leq \dfrac{(0)(1-0)^3}{180(2)^4} \\ \leq 0$ The actual error is approximately $[121.5000006-121.5 ] \approx 6 \times 10^{-7}$, which is less than $10^{-6}$. We see that: Error $(S_2)=0$ So, $S_2$ gives the exact value of the integral.