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

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

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

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

$$ \int_1^4\left(x+\sqrt{x}+\frac{1}{x}\right) d x-\int_1^{2 \log 2} d x= $$