The correct option is A 8πf ( 2 ) x→π #160; 4 #160; lim ∫ _ 2 ^ sec^ 2 x f(t)dt x^ 2 π ^ 2 16 #160; Applying L'hospital rule #160; ...

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Vn Method

limx→π4 ∫2x...

Question

$lim x \to \frac{π}{4}$ $\int_{2}^{{sec}^{2} x} \frac{f (t) d t}{x^{2} - {\frac{π}{4}}^{2}}$

\frac{8}{π} f (2)

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\frac{2}{π} f (2)

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\frac{2}{π} f (\frac{1}{2})

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4 f (2)

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Solution

The correct option is A $\frac{8}{π} f (2)$
$l i m x \to \frac{π}{4} \frac{\int_{2}^{s e c^{2} x} f (t) d t}{x^{2} - \frac{π^{2}}{16}}$
Applying L'hospital rule
$l i m x \to \frac{π}{4} = \frac{2 tan x {sec}^{2} x f ({sec}^{2} x)}{2 x} = \frac{8}{π} f (2)$

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