Mathematics Question from JEE Main 2026 · 24 January, Shift 1

Let a differentiable function $f$ satisfy

$$\int_0^{36} f\!\left(\frac{tx}{36}\right)dt=4\alpha f(x).$$

If $y=f(x)$ is a standard parabola passing through the points $(2,1)$ and $(-4,\beta)$, then $\beta^{\alpha}$ is equal to