$$\int_\limits0^2[x] \mathrm{d} x+\int_\limits0^2|x-1| \mathrm{d} x=$$

(where $$[x]$$ denotes the greatest integer function.)

$$\int_\limits{\frac{\pi}{6}}^{\frac{\pi}{2}} \frac{\operatorname{cosec} x \cdot \cot x}{1+\operatorname{cosec}^2 x} d x=$$

$$\int_\limits0^2|2 x-3| d x=$$

If $$\int_\limits0^a \sqrt{\frac{a-x}{x}} d x=\frac{k}{2}$$, then $$k=$$