It is given that $\frac{d}{d t}(t \log t-t)=\log t$, then $\exp \left(\int_0^1 2 x \log \left(1+x^2\right) d x\right)=$

$$ \int_0^{2 a} f(x) d x= $$

$$ \int_1^2 x \sqrt{4-x^2} d x= $$

If $[x]$ denotes the greatest integer function of $x$ and

$$ \int_{-3 / 2}^{3 / 2}[2 x-3] d x=k, \text { then }\left|k+\frac{1}{2}\right|= $$