Let {\f} be a differentiable function defined on [0, \frac{\pi}{2}] such that {\f}( {\x})>0 and f(x)+\int_{0}^{x} f(t) \sqrt{1- (\log _e f(t)) ^2} \dt=e, \forall x \in [0, \frac{\pi}{2}]. Then (6 \log _e f (\frac{\pi}{6}) ) ^2 is equal to___ [24-Jan-2023 Shift 2]

Definite Integrals Part 2

Section: Mathematics

Question : 3 of 100

Marks: +1, -0

Let f be a differentiable function defined on [0,‌

] such that f(x)>0 and f(x)+

∫

f(t)√1−(logef(t))2‌dt=e,∀x∈[0,‌

].
Then (6logef(‌

))2 is equal to___

[24-Jan-2023 Shift 2]

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