Let f:[-(π)/2, (π)/2] → R be a differentiable function such that f(0)=1/2. If the lim_x → 0 (x ∫_0^x f(t) d t)/(e^x^2-1)=α, then 8 α^2 is equal to:

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