d
\(dT = dm\,{\omega ^2}x\, = \left( {\frac{m}{l}} \right)\,dx\,.\,{\omega ^2}x\, = \frac{{m\,{\omega ^2}}}{l}\, [x \,d \,x]\) 

\(\int\limits_x^l {dT} = \frac{{m\,{\omega ^2}}}{l}\int\limits_x^l {x\,dx} \)

\(T = \frac{{m{\omega ^2}}}{l}\left[ {\frac{{{x^2}}}{2}} \right]_x^l\)

\(\therefore T = \frac{{m\,{\omega ^2}}}{{2l}}\left[ {\,{l^2} - {x^2}} \right]\)