Let $f$ be a differentiable function defined on $\left[0, \frac{\pi}{2}\right]$ such that $f(x)0$ and $f(x)+\int_0^x f(t) \sqrt{1-\left(\log _e f(t)\right)^2} d t=e, \forall x \in\left[0, \frac{\pi}{2}\right]$ then $\left(6 \log _e f\left(\frac{\pi}{6}\right)\right)^2$ is equal to

Question

Let $f$ be a differentiable function defined on $\left[0, \frac{\pi}{2}\right]$ such that $f(x)>0$ and $f(x)+\int_0^x f(t) \sqrt{1-\left(\log _e f(t)\right)^2} d t=e, \forall x \in\left[0, \frac{\pi}{2}\right]$ then $\left(6 \log _e f\left(\frac{\pi}{6}\right)\right)^2$ is equal to

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Let \(f\) be a differentiable function defined on \(\left[0, \frac{\pi}{2}\right]\) such that \(f(x)>0\) and \(f(x)+\…

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Let \(f\) be a differentiable function defined on \(\left[0, \frac{\pi}{2}\right]\) such that \(f(x)&gt;0\) and \(f(x)+\…

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Let \(f\) be a differentiable function defined on \(\left[0, \frac{\pi}{2}\right]\) such that \(f(x)>0\) and \(f(x)+\…