Chris, I strongly suggest you get in touch with Gustav Delius and his project.
$$
\Bigsum_{i=\1}^{n-\1}\frac1{\Del~x}\Bigint_{x_i}^{x_{i+\1}}\{\frac1{\Del~x}\big[(x_{i+1}-x)y_i^{5$\star}\big]-f(x)\}^\2dx$$
Mathematics tools
Linking Moodle with a CAS
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