$[14$ Points$]$

$$ SCALCET$97\mathrm{.}7\mathrm{.}027.$

Find the approximations $T_n,M_n,$ and $S_n$ for $n=6$ and $12.$ Then compute the corresponding errors $E_T,E_{Np}$ and $E_S.($Round your answers to six decimal places. You may wish to use the sum command on a computer algebra system.$)$

${\displaystyle \underset{0}{\overset{2}{}}}38x^{4}dx$

$\backslash$table$[[n,T_n,M_n,S_n$