A) 24
B) 36
C) 12
D) 18
Correct Answer: D
Solution :
\[\underset{x\to 2}{\mathop{\lim }}\,\int_{6}^{f(x)}{\frac{4{{t}^{3}}}{x-2}}dt=\underset{x\to 2}{\mathop{\lim }}\,\frac{\int_{6}^{f(x)}{4{{t}^{3}}dt}}{x-2}\] \[=\underset{x\to 2}{\mathop{\lim }}\,\frac{4{{[f(x)]}^{3}}}{1}f'(x)=4{{[f(2)]}^{3}}.f(2)\] \[=4{{(6)}^{3}}.\left( \frac{1}{48} \right)=18\]
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