Let $f$ be a differentiable function satisfying $f(x) = 1 - 2x + \int\limits_0^x e^{(x-t)} f(t)\,dt$, $x \in \mathbb{R}$ and let

$g(x) = \int\limits_0^x (f(t) + 2)^{15} (t - 4)^6 (t + 12)^{17}\,dt$, $x \in \mathbb{R}$.

If $p$ and $q$ are respectively the points of local minima and local maxima of $g$, then the value of $|p+q|$ is equal to ________.

$$ \text { The value of } \sum\limits_{r=1}^{20}\left(\left|\sqrt{\pi\left(\int\limits_0^r x|\sin \pi x| d x\right)}\right|\right) \text { is } $$

Let a differentiable function $f$ satisfy the equation $\int_0^{36} f\left(\frac{t x}{36}\right) d t=4 \alpha f(x)$. If $y=f(x)$ is a standard parabola passing through the points $(2,1)$ and $(-4, \beta)$, then $\beta^\alpha$ is equal to $\_\_\_\_$ .