a) $\int\limits_2^4 {\frac{{{x^2}}}{6}\,dx} \,\,\,\,\,\,\,\,\,\,\,( = \left[ {\frac{{{x^3}}}{{18}}} \right]_2^4)$

$ = \frac{{{4^3}}}{{18}} - \frac{{{2^3}}}{{18}}$

$ = \frac{{28}}{9}$

b) $\int\limits_2^m {\frac{x}{6}dx} \,( = \left[ {\frac{{{x^2}}}{{12}}} \right]_2^m)$

$\frac{{{m^2}}}{{12}} - \frac{{{2^2}}}{{12}} = 0.5$

$m = \surd 10$ oe

c) $\int\limits_3^4 {\frac{x}{6}dx} \,\,\,\,\,\,\,\,\,( = \left[ {\frac{{{x^2}}}{{12}}} \right]_3^4 = {\raise0.5ex\hbox{$\scriptstyle 7$}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{$\scriptstyle {12}$}})$

${\left( {''{\raise0.5ex\hbox{$\scriptstyle 7$}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{$\scriptstyle {12}$}}''} \right)^2}$

$ = {\raise0.5ex\hbox{$\scriptstyle {49}$}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{$\scriptstyle {144}$}}$ or $0.340{\text{ }}\left( {3{\text{ }}sfs} \right)$