The area of the region bounded by the curve $y=|x-2|$ between $x=1, x=3$ and X -axis is ……

$$ \int_{-1}^3\left(\tan ^{-1}\left(\frac{x}{x^2+1}\right)+\tan ^{-1}\left(\frac{x^2+1}{x}\right)\right) d x= $$

Let A be a non-singular matrix of order n and $|A|=k$, then $(\operatorname{adj} A)^{-1}$ is

If $f(x)= \begin{cases}\frac{8^x-4^x-2^x+1^x}{x^2}, & \text { if } x>0 \\ \mathrm{e}^x \sin x+\mathrm{i} x+\lambda \log 4, & \text { if } x \leqslant 0, \mathrm{i} \in \mathbb{R}\end{cases}$ continuous at $x=0$, then the value of $500 \mathrm{e}^\lambda$ is