(a) Use Simpson's Rule, with n = 6, to approximate the integral ∫₀¹ 8e⁻³ˣdx.
(b) The actual value of ∫₀¹ 8e⁻³ˣdx.
(c) The error involved in the approximation of part (a) is Es = ∫₀¹ 8e⁻³ˣdx - S6.
(d) The fourth derivative f⁽⁴⁾(x). The value of K = max |f⁽⁴⁾(x)| on the interval [0, 1].
(e) Find a sharp upper bound for the error in the approximation of part (a) using the Error Bound Formula |Es| ≤ K(b-a)⁵ / (180n⁴).
(f) Find the smallest number of partitions n so that the approximation Sn to the integral is guaranteed to be accurate to within 0.0001.
n =