Let f:R→R be a differentiable function and f(1)=3, then limx→1∫3f(x)2tdtx-1=

limx→1∫3f(x)2t dtx−1=limx→1d dx∫3fx2tdt1                 by LH rule                                                            =limx→12f(x)f'(x)1     by Newton's Leibnitz rule    =2f1f'1=6f'1