Question

Integrate ${\int }_0^{2\left[x\right]}\left\{\frac{x}{2}\right\}dx$

Answer 1

${\int }_0^{2\left[x\right]}\left\{\frac{x}{2}\right\}dx=2\left[x\right]{\int }_0^1\left\{\frac{x}{2}\right\}dx$ As $\left\{\frac{x}{2}\right\}=\frac{x}{2}\forall xϵ[0,1]$

$=2\left[x\right]{\int }_0^1\frac{x}{2}dx=\frac{2}{4}\left[x\right][x^2{]}_0^1$

$=\frac{1}{2}\left[x\right]$