Let \(f:\left[-\frac{\pi}{2}, \frac{\pi}{2}\right] \rightarrow R\) be a differentiable function such that \(f(0)=\frac{1…

Let \(f:\left[-\frac{\pi}{2}, \frac{\pi}{2}\right] \rightarrow R\) be a differentiable function such that \(f(0)=\frac{1}{2}\). If the \(\lim _{x \rightarrow 0} \frac{x \int_0^x f( t ) dt }{ e ^{x^2}-1}=\alpha\), then \(8 \alpha^2\) is equal to :

[JEE Main 2024, 30 Jan (Shift 1)]