Chapter 8.8, Problem 70E

Let f (x) = $e^{-x^2}$

1. a. Find a Simpson’s Rule approximation to ${\displaystyle {\int }_0^3{e}^{-x^2}}$ dx using n = 30 subintervals.
2. b. Calculate f ⁽⁴⁾(x).
3. c. Find an upper bound on the absolute error in the estimate found in part (a) using Theorem 8.1 (Hint: Use a graph to find an upper bound for |f ⁽⁴⁾(x)| on [0, 3].)