Past exam of the year 1 of the computer science course of the University of Oxford / 2018 / Discrete mathematics, continuous mathematics, and probability / 6 / e / Solution

With unit strip width, the composite trapezoidal rule givesFor Simpson's rule, the even integer arguments are the odd-numbered interior grid positions. ThereforeThe requested two-decimal answers are $T_{24}\approx 0.79$ and $S_{24}\approx 0.75$. The supplied component sums are individually rounded; they should not be treated as exact simultaneous identities. Computing from the original function gives approximately $0.786685$ and $0.748700$, respectively, with the same two-decimal results.