Let
\Xi(x)=2012(x-2)^{2}+278(x-2) \sqrt{2012+e^{x^{2}-4 x+4}}+139^{2}+\left(x^{2}-4 x+4\right) e^{x^{2}-4 x+4}
find the area of the region in the x y-plane satisfying:
\{x \geq 0 \quad \text { and } \quad x \leq 4 \quad \text { and } \quad y \geq 0 \quad \text { and } \quad y \leq \sqrt{\Xi(x)}\}