Let $f:R \to R$ be a differentiable function having $f\left( 2 \right) = 6$, $f'\left( 2 \right) = \left( {{1 \over {48}}} \right)$. Then $\mathop {\lim }\limits_{x \to 2} \int\limits_6^{f\left( x \right)} {{{4{t^3}} \over {x - 2}}dt} $ equals :

Question

Let $f:R \to R$ be a differentiable function having $f\left( 2 \right) = 6$,
$f'\left( 2 \right) = \left( {{1 \over {48}}} \right)$. Then $\mathop {\lim }\limits_{x \to 2} \int\limits_6^{f\left( x \right)} {{{4{t^3}} \over {x - 2}}dt} $ equals :