A) \[\frac{8}{\pi }f(2)\]
B) \[\frac{2}{\pi }f(2)\]
C) \[\frac{2}{\pi }f\left( \frac{1}{2} \right)\]
D) \[4f(2)\]
Correct Answer: A
Solution :
[a]: Let\[L=\underset{x\to \frac{\pi }{4}}{\mathop{\lim }}\,\frac{\int\limits_{2}^{{{\sec }^{2}}x}{f(t)dt}}{{{x}^{2}}-\frac{{{\pi }^{2}}}{16}}\] Applying L? Hospital rule \[L=\underset{x\to \frac{\pi }{4}}{\mathop{\lim }}\,\frac{f(se{{c}^{2}}x).2se{{c}^{2}}x\tan x-0}{2x}\] \[L=\frac{f(2).4}{\pi /2}=\frac{8f(2)}{\pi }.\]You need to login to perform this action.
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