Past exam of the options I course of the University of Oxford / 2012 / P / P2 / c / Solution

Apply the first Richardson extrapolation step to the two computed approximations:The exact integral is $I={\int }_0^1{x}^{4}dx=1/5$, so the actual absolute error isThus the requested strict error bound is verified directly. This first extrapolation of trapezoidal approximations is also the one-panel Simpson's rule value on the three nodes $0,1/2,1$.