Question $4[10$ marks$]$

For

${\displaystyle \underset{2}{\overset{3}{}}}\sqrt[\phantom{2}]{lnx}dx$

$($a$)$ Establish the number of sub$-$partitions $N$ needed for the trapezium rule to assure third decimal accuracy in the approximation of the integral.

$($b$)$ Calculate the trapezium approximation for $N$ intervals.

$(5)$

$1$