The remainder can be rewritten as \[-\frac{h^{3}}{12} \sum_{i=0}^{n-1} f^{\prime \prime}\left(\xi_{i}\right)=-\frac{n h^{3}}{12}\left\langle f^{\prime \prime}\left(\xi_{i}\right)\right\rangle \nonumbe...The remainder can be rewritten as \[-\frac{h^{3}}{12} \sum_{i=0}^{n-1} f^{\prime \prime}\left(\xi_{i}\right)=-\frac{n h^{3}}{12}\left\langle f^{\prime \prime}\left(\xi_{i}\right)\right\rangle \nonumber \] where \(\left\langle f^{\prime \prime}\left(\xi_{i}\right)\right\rangle\) is the average value of all the \(f^{\prime \prime}\left(\xi_{i}\right)^{\prime}\) s.
