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Let $f:R \to R$ be a differentiable function having $f(2) = 6, f'(2) =(\frac{1}{48}) $. <br> Then $\displaystyle\lim_{x \to 2} \int_6^{f(x)} \frac{4t^3}{x-2} dt$ equals :


( A ) 36
( B ) 24
( C ) 12
( D ) 18

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